If the Germans have committed their resources for the war against the Soviets, rather then putting them into the build-up for the war against the Anglo-Americans as they were in OTL, none of these objections are fatal: the Germans would actually have the replacements to make up for their August-September losses against the Soviet counter-offensive on the Moscow axis (and the Soviet losses also heavily weakened the Soviet forces along the Moscow-axis, setting up the Soviets for their own defeats at Vyazma and Bryansk), the whole reason was because they were taking more limited actions to destroy Soviet forces in exposed positions as I proposed rather then try to do the impossible and win the war in a single swoop (and again, their victories there conditioned the success at Vyazma and Bryansk of their subsequent offensive toward Moscow), and the claim the Germans defensive action won't have outsized impact on Soviet combat capability is both unsubstantiated and in contradiction to history: when the Germans inflicted just such a defeat upon the Soviets at 2nd Kharkov, the Soviets were so badly weakened that it opened the door to the subsequent German advance to the Caucasus and Stalingrad. While the campaign would indeed be a long-costly slog, as I already observed that was always going to be the case given the size and strength of the USSR. The German belief that it wouldn't was predicated both on the USSR being weaker then it was and themselves being stronger then they actually were. The Germans refusal to accept this and continuous attempts at quickly knocking out the USSR in one season to is what led to their defeat.
I agree that it was a serious mistake to prioritize building new divisions rather than keeping existing ones in combat up to strength, especially once it was clear the campaign was going to be longer and harder than anticipated.
Certainly Soviet losses in the offensives in August-September (not just on the Moscow axis) weakened them, but it was more than just their losses that did them in, as the Germans themselves were reinforced with fresh divisions, the 2nd and 5th Panzer, who were fully up to strength and probably as strong individually as the average Panzer corps at the time even with the limited reinforcements they got in September, which against the forces the Soviets had arrayed against them coupled with operational surprise yielded big benefits in the October pockets.
The limited operations along the Moscow axis in October-September was in response to the series of threats they faced as a result of the heavy offensives the Soviets launched that pushed serious bulges into their lines. They were a defensive reaction rather than per a specific strategy/operational plan. The post-Smolensk pocket period was supposed to be a pause on that axis to clean up the flanks with the better part of their mobile forces and refit the worn down divisions left behind before the push on Moscow, but the Soviets denied them that opportunity and instead wore them down even worse and the exchange rate was considerably worse than the Germans got earlier and later when attacking. The comparison with 2nd Kharkov/Case Blue isn't necessarily similar because the Soviets took proportionally much worse losses there than during their offensives in August-September 1941, while inflicting worse losses on the Germans in 1941 than in 1942. I mean Glantz claims 100k casualties in August-September 1941, while 2nd Kharkov only inflicted 20k-30k casualties on the Germans.
The Germans were left much stronger in 1942 and the Soviets FAR weaker in Ukraine than they were on the main axis, plus after 2nd Kharkov the Germans launched two more preparatory offensives before Case Blue after Kharkov that weakened them even further, while Stalin denied them replacements to shore up the Moscow defenses. Meanwhile in October 1941 the Soviet forces along the Moscow axis had gotten reinforcements and were stronger in raw numbers and proportionally than the Soviet forces left in Ukraine in June 1942 right before Case Blue.
As to winning the war outright in one campaign, that wasn't going to happen, but taking Moscow would have been a moral wound to the USSR that would have started the process of unraveling the Soviet regime and it's ability to continue to resist. Of course IMHO October is took late to pull that off and while at that point the best bet was to launch the October pocket offensives and then transition to defense when the weather made advancing impossible, as any further effort would run into all the reinforcements the Soviets had been able to mobilize and bring in the meantime, which were too much to overcome with the resources and time left before winter hit.
IMHO, as we've argued before and would only be retreading ground we covered in previous threads, launching Moscow instead of the Kiev and Leningrad offensives in August-September was really the only way to have enough time to take Moscow without the weather intervening and at a point when Soviet forces were weaker than they would become by October.
https://www.alternatehistory.com/forum/threads/operation-typhoon-september-1941.438921/
While it is true that in the context of Germany being still at war with the UK with heavy US support and eventual entry, a multi-year campaign with a maximum effort against the USSR that consumes all the Reich's reserves is likely to end in German defeat anyways regardless of what happens in the East, that was liable to always be the case in such a context. The smart choice there is not to attack the Soviets at all.
Agreed, turning East was a terrible strategic choice even at the time without hindsight.
That said even with the defeat of the USSR, which was potentially possible with better choices in the 1941 campaign, it is still more likely than not that with US entry Germany is still probably going to lose the war, just on a longer time frame and much higher losses to the Wallies.