He could always
try, though he isn’t likely to succeed.
Why though, it might be asked. After all, they’re the Qing, aren’t they? The dynamic and active dynasty that invited Jesuits and generally stayed at the forefront of military and geographic science during this time-period? If I may, I would like to present why I believe, in my humble opinion, this wouldn’t work out, which is a mixture of both the reasons against the campaign in the first place and why the long-term feasibility of the conquest is dubious. Apologies beforehand for all the text.
First of all, there’s a crucial difference between the Dzungar and the Kazakhs, even though they’re both neighboring nomadic powers. The Dzungar were Tibetan Western Mongols, with imperial ambitions and links to the Tibetan lamas. The Qing invested a tremendous amount of effort into presenting themselves as legitimate inheritors of the Genghisid imperial tradition and as patrons of Tibetan Buddhism, in order to link themselves to and win the allegiance of the Mongols, succeeding the most with the Eastern Mongols. The Dzungar, aiming to unify the Mongols and with their strong links to the Tibetan lamas, represented a direct threat to the Qing imperial project because they too could claim to be rightful inheritors of the Genghisid imperial tradition and patrons of Tibetan Buddhism, beyond the fact they were situated uncomfortably close to the 18 provinces and were raiding them. As long as the Dzungar remained, they could always call upon rebellious Mongols and point out their commonalities and religious links and thus threaten the Qing hold on the steppe. This wasn’t just Qianlong thinking he wanted to solve this problem in one stroke; the Qing invested themselves into a multi-generational effort at subjugating Tibet and weakening the Dzungar, of which Qianlong’s campaign was just the- admittedly impressive- culmination. The Kazakhs, on the other hand, were Muslim Turkic nomads without any real interest in trying either to threaten the Qing hold on Tibet or even for that matter presenting themselves as the next re-unifiers of the Mongol empire. They wanted trade, and the Qing were happy to engage in tribute with them. From the Qing side, there is no reason to engage in a long and arduous campaign against a power that does not threaten their interests. If the Kazakhs did engage in war against the Qing, then yes, it would be possible to see the Qing engage in said long and arduous campaign against them, but even then, the Qing have more pressing issues back home in China and would most likely sue to for a return to status quo ante bellum, or a subservient Middle zhuz at the very most. Against the Dzungar, the Qing were waging a war to bring about the final victory of their imperial ambition on the steppe, and after what was effectively their genocide of the Dzungar, that was as far as they needed to go. Even if Qianlong decided to push westwards during the Dzungar campaign, which he nearly did, the most it would amount to would probably be a few expeditions and then probably peace as the two realize they have nothing to gain from it. The Senior zhuz itself is effectively split between the Qing and Kokand without any real problems.
Second, the khanates and emirates. Kokand is not a threat. In fact, the Qing worked out their differences and let Kokand alone, which acted as a kind of passive-aggressive frenemy to the Qing. There is no reason, unless Kokand for some reason feels threatened and attacks the empire, for Qianlong to engage in a campaign against them. Same for Bukhara. Both of these powers paid tribute, neither really engaged in attacks against the Qing, and even when Kokand harbored the Khojas, the Qing often preferred to solve the Khojas themselves and grudgingly overlook the Kokandi involvement; while admittedly, this was under some of their less vigorous moments, and it is probable that Qianlong could act against Kokand more vigorously, and would if the Khojas had presented a really serious threat, there is little reason the Khojas would try and do this with Kokandi blessing if the Qing were that strong and vigorous in the first place. Khiva not only never presented a threat, it is even further away, leading to the next point.
Third, logistics. Balkhash is an incredible distance not only from Mukden, but more importantly from Beijing and even Xi’an and Lanzhou. While the Qing did have amazing logistics in the campaign in Xinjiang, the simple fact is that beyond Kashgar, it gets awfully difficult to project power. Balkhash was conquered because it was part of the Dzungar khanate to begin with, and even then, the Qing tolerated Cossack forts and camps in the overall border region, and even areas nominally in Xinjiang, such as Zaysan. The Aral Sea is an even greater distance than that. Presuming they could even fight the Kazakhs that far away, how are they going to hold it? They’re going to have transport men, supplies and weapons over vast distances, without much in the way of roads and under constant threat of attack in pretty unfriendly terrain, to which the bulk of their armies are not used to. Even though the Qing armies at this time were still pretty darn good, they aren’t likely to pull off such a feat. The Caspian is this many times over, without even counting the other issue of hearts and minds.
Fourth, religion. The Dzungar had to deal with the fact that half of their empire was effectively in revolt against them, thanks to them being Buddhist Mongols and the Tarim being Muslim Turkic, in addition to high taxes. The Tarim was happy to switch sides, a minor revolt notwithstanding, to the Qing, which they preferred to their old Dzungar masters- the new heathen, basically, was preferable to the old one. There is nothing of that out west. All of the powers can call upon a natural justification for war, which is going to lead to the Qing facing tough opposition, against people who have been living in their own states, under their own laws and can call upon religious brethren-in-arms, as they are suddenly being invaded by the heathens from the east. While it is true that the Qing were able to be a chameleon of rulership- khans, patrons of Tibetan Buddhism, Confucian emperors, and having mosques honor their name- this is unlikely to fly against people who already have a conception of the Qing as heathens, and especially so when they are at war against them.
Fifth, Russia. Russia is not going to let someone just waltz into what is effectively their sphere of interest, especially not after they have already decided that they’re going to work out their differences through negotiation. The Qing went to great lengths to show the Russians that the Senior zhuz was in fact their vassal, and even the Middle zhuz, but importantly, they did so while acknowledging that the Junior zhuz was in the hands of the Russians; when they had disagreements, such as over Ablai, they and the Russians negotiated under a framework that recognized the Kazakh zhuz as effectively divided between them, even though where the dividing line was located was always up for question. But they’ve already gone to war with the Russians in the past- and though they might technically have won that time- they are not in an appetite for more, and the Qing have already decided to honor the Russians as geopolitical equals in practice if not in name. It’s a mere thirty years after Kyakhta, they’ve already worked out their differences and spheres, and have a framework for renegotiation and peaceful settlement of their disputes- why waste all of that now? For glory? Qianlong was a vain man, sure, but he wasn’t foolish, at least not that much.
Sixth, ‘domestic issues’. Beyond the simple fact of funding, how is Qianlong going to justify this to the scholar-officials? Against the Dzungar, the Qing made a great propaganda effort at presenting themselves as civilizing the Western Regions and reintegrating areas from the Han and Tang times, but even then, scholar-officials often regarded being sent to Xinjiang as a form of exile- which it in may cases often was- because it was still seen as outside of ‘civilization’. There’s not even that here with the areas beyond Kashgar- while the Han and Tang held control of the Tarim for centuries, the Tang alone only held control over areas beyond that for a few decades. Even if they try and pull the civilizing card, most scholar-officials are likely to interpret the fact that the Kazakhs and khanates were willing to offer tribute as good enough already. There are no resources which the Qing urgently need, and unless they have attacked the empire, for the scholar-officials, there is simply little to no reason for Qianlong to start attacking states that by all accounts are happy to give tribute; they will likely send memorial after memorial to the throne urging him to show restraint worthy of a sage-ruler. Back home, there are rebellions, internal campaigns inside frontier areas, and even- stretching the definition of ‘domestic’- campaigns against states closer to home, and most importantly, the perennial rebellions that plague the empire are still going to break out, whether it is late during Qianlong’s reign or under that of his successors, which will necessitate a retreat of imperial power from the frontier.
Finally, Qianlong himself. Qianlong was great and all, but the last half of his reign was a disappointment. What seems like 30 more years is in fact perhaps 15, or 20 at most. Furthermore, the issues that plagued them because of Qianlong’s own personality are not going to go away because of him engaging in some campaigns in the far west- if anything, considering the cost that they’re going to be, they’re going to increase. He’s still overseeing a Qing expanding in the Shan regions, and sooner or later he and the Konbaung kings are going to get into a dispute over which Shan chieftain owes allegiance to who; the Vietnamese are probably still going to see the Le dynasty fall, upon which Qianlong will likely jump at the opportunity to restore Jiaozhi and probably get defeated by the Tay Son; and most importantly, the rebellions are still going to break out, especially if Qianlong becomes as tired, weary and fatigued as he did OTL. With Qianlong, there’s still going to be an exhausted treasury, other campaigns he wants to execute, and thus further probable failures in Jinchuan, Myanmar and Vietnam, wide-spread corruption even if it won’t necessarily be under Heshen, and rebellions that will effectively gut the treasury. This is not to say that Qianlong couldn’t try, but even if he manages the superhuman effort to conquer the far west and also stay alert to the end, he’s going to leave his successor with even more problems- more extension of the empire’s administrative and military capabilities, more rebellious subjects, more borders inviting trouble from far-away opponents.
If any of these powers- the Kazakhs, Kokand, Bukhara- engaged in war against the Qing, then yes, the Qing would strike at them. If any of them do so when Qianlong is in his prime, then yes, it is likely that they will be conquered, though I’d say that Kokand, and a very loose Middle zhuz allegiance, is the feasible upper limit. But why would he venture so far out, and further, if he is not attacked and wants to do all the other things he wanted to do? If he tries, he will likely fail. If he tries because he has been attacked, he will likely stop before he reckons that he’ll become over-stretched, which is a far distance from Khiva and likely means punishment and annexation of the offending party, either Kokand, or the Middle zhuz at most. And even if he should succeed, there is no guarantee his successors will be able to keep it- actually, considering the quality of his successors, this might just hasten the Qing decline.
OTOH if they have to fight the Russians or the persians in central asia on a regular basis, their military might not stagnate
While I agree with Perdue’s idea that the Qing likely needed some kind of incentive to stay on the edge militarily, it would probably be better to look at a surviving Dzungar khanate as he suggested, or a Qing dynasty that decides to be far more active on its frontiers and is successful in doing so; but probably not through something as demanding as a campaign against Bukhara or Khiva, and certainly not defending those areas from the Persians or Russians, the former having advantages in both distance, logistics, morale and support, or the latter, who they already have a working relationship with and who are close to their ancestral heartland.