Why do Eastern European boxers stay in one weight class for their career?

Probably they don't get as fat. The populations simply aren't as fat in daily life too.
The level of fatness in Murica has never been seen on this earth.

 

A good fighter knows his limits and what works best for him.

Take Beterbiev. He might gain some power if he moves up to cruiserweight, but at what cost? He might lose some speed and stamina with the extra bulk. At 6'0, he'd honestly be on the smaller side for that division with plenty of guys who are 6'2-6'3, so he might struggle needing to adapt to a swarming style. Even the best swarmers still take a lot of punishment no matter how good their defense and technique are so he probably prefers to just stay in his natural element. Cutting weight would also not be ideal as he might be too weak at 168 killing himself to train down.