With less advanced weapons in the 1600s though, wouldn't the Russians have taken some pretty extreme casualty ratios against Kazakh cavalry if they led extended campaigns into Kazakhstan that early?
So I don't see how that's justifiable. There are literally no major military engagements from the 17th c. where Russians took unfavourable casualty ratios in North/Central Asia/anywhere on the Steppes.
They were however perfectly capable of melting down logistically, as happened with Alexey Mikhailovich's Derbent expedition, Golitsyn's two Crimean expeditions, and even Prince Bekovich-Cherkassky's Khiva expedition. Logistics is the real issue.
Russian Streltsy infantry would have had an extremely tough time on the open steppe but in OTL the Steppe was mostly conquered by the Cossacks who while not exclusively cavalry like the steppe people's were very cavalry heavy.
So the Streltsy did fine against horse armies, because they almost always fought from behind fortifications, either static or in the form of a gulay-gorod (war wagons, basically). Siberia was full of streltsy serving in garrisons too, as well as service cossacks. Other Russian forces in Siberia included service Tatars, local people like Buryats/Bashkirs/Evens/Yakuts (who often enrolled in Cossack or Streltsy ranks anyway later in return for salaries in form of sugar/flour/gunpowder/tea/cloth), and armed western POWs who were collectively known as "Lithuanians" (who were generally released to return home after a set number of years, but many of them chose to settle and also enroll in the cossacks).
Most of them fought in whatever way they were used to, and generally did well, including the native Siberians.
So why? Well, for starters, Russians had cannons to support the native arms. Bukharans had cannons too, but Russians had more and better. The cannons were placed onto the walls of an ostrog, which was a timber fort with a blockhouse and say, three or more walls. The Russians were very proficient at building these quickly from pre-cut, pre-fabricated timber, because that's how they settled the European steppes too. Sometimes the forts were taken by say, the Oirats or the Qing or whoever, but mostly they were too much for any local people to handle. Whenever the Russian forces in the area were badly enough outnumbered, they retreated to an ostrog and waited for reinforcements.
So what prevented the Russians from plonking forts all over Kazakhstan in the 17th c.?
Two things: first, how? Timber was either locally sourced or floated down a river, along which the Russians expanded anyway. Not a lot of timber on the Kazakh steppe, and not a lot of rivers either. Problem.
second, why? Russian expansion into Siberia was motivated by capturing the fur tax which provided an extremely high level of return for the crown directly. It was basically a cash crop without major investment. The Russians sought it out greedily with various degrees of sometimes-cooperation, sometimes brutal mistreatment of the locals. Salt and iron brought the Russians into the Urals, but furs took them to the Pacific.
There isn't much furs in Kazakhstan. Pastoral economies would be vulnerable and low-return. Why bother? Even as agricultural land, it's nothing compared to the Volga/Don which were at the time just being internally settled too. If it was good agricultural land, be sure they'd at least try. They did in Western Siberia and in Dauria risked a war with the Qing just to find some land to grow wheat.
By the 19th c. of course the fur-centric approach is long gone, and the farming techniques are more advanced, which is why the attitude change towards the steppe.
In OTL they spent most of the 17th and 18th centuries either fighting in Russia's various internal problems, against the Commonwealth or against the Crimeans. Different Tsars and a different international situation could see them directed against the Kazakhs. Once again I'm not saying this is likely, the Ukrainian and North Caucus steppe's are more obvious places for expansion but if those routes are unavailable or unattractive you could see a more directly Eastward focus.
Another thing to consider is Russia's diplomacy. In the 16th c. they allied with the Bashkirs, in the 17th c. they were allied with the Kalmycks, in the 18th. both the Kalmycks and Kazakhs. Every time they tried to settled lands belonging to allies, however, the alliances broke down. This was undesireable.
By the time the Siberian Line Host is formed (in 1808) all those alliances are largely irrelevant because the allies are not strong enough to be useful, and the Russians start grabbing clay.