This is partially due to eastern regions of Europe being better for cavalry and partially due to the fact that by XVIth century the heavily armoured lancer was seen as technologically inferior and expensive, and this is at least half correct. You are correct that Husaria were expensive and that they required long amounts of training, but this in itself is not good thing. Modernisation requires quicker training and more cost-effective equipment, while the Polish Husaria were the greatest heavy cavalry of their time they could only work in a time and place where the nobility were so excessively rich as to afford the expensive armaments; not exactly a cost-effective system considering that they were beaten by some Ukrainian Cossacks and Tatars.
How do you mean?
They existed from 1630's, the original Polish-style hussars used in Russia were trained by immigrants from the Commonwealth not unlike the other "foreign order" regiments being trained by foreigners. But Russian hussars, or at least the XVIIth century type based of Polish Husaria, were never used in great number; their lack of widespread use has more to do with being too expensive and long to train for small benefit they offered over the reiter-type cavalry which most were transferred too. The last ones were in the Novgorod Regiment until it was removed by Peter the Great during his modernisation of Russian military because by that time they were very outdated.
Interesting you should say that, because even before Gustavus reformed his cavalry and removed the caracole the Polish forces hadn't really struck decisive victories against the Swedish.
But honestly, Imposter is kind of sick of the excessive amount of Husaria worship that you see on the internet, yes, they were one of the best heavy cavalry formations of their time, but in the end they weren't demigods and their side eventually lost the war.