But even then, the KV tanks were only a small part of their arsenal; the Russians had settled on three different categories of tanks: mobile tanks (their very fast BT tanks using Christie suspension), medium tanks, and heavy tanks. The latter category included the KV-1 and KV-2 tanks, and that was the smallest and most expensive group, but also the group that would always be at the center of any attack or defense.
The reason the T-34 was such an important tank, is that it combined aspects of all three categories; it was intended as a medium tank, but it had Christie suspension like the BT tanks, making it faster than most other medium tanks. And due to its sloping armour, it was almost as tough as a heavy tank (against tanks at least; it was vulnerable from the air). This combination made it the precursor of the Main Battle Tank.
Remember the Nazi's invasion depended on their multiple tank groups making a very fast progress through this country, until they reached Moscow. It was not total war combat until much later.
Many of them were halted or destroyed when they faced a single inantry group backed by a KV-1. That was enough to cripple their invasion (among the other equivalent Russian tanks).
If you don't believe my account I highly recommend this book which is the best coverage of the eastern front, and questions much of the popular accounts of WW2 with some great research and plenty of citation:
https://www.amazon.com/Operation-Barbarossa-Germanys-Cambrid...
The real key to the Soviet win is that they could endure 3:1 loss ratios and still outdeploy the Nazis at better than 3:1.