Im not sure stalemate accounts for most draws at the highest level.

Getting rid of check does make for a better game at beginner levels.

It's both easier to teach and leads to exciting finishes ss noobs hang their king.

Trying to force or avoid stalemate is a huge motive in top level endgames though regardless of whether they actually end in stalemate or not.

There are a lot of endgames that are drawn because of stalemate though. Many pawn endgames ( e.g. pawn and king against lone king) are drawn because of stalemate, but would be a win in most cases if stalemate didn't exist.

You likely didn't mean to imply all king+pawn vs king endgames are drawn, but to clarify for the layman reading, many are winnable.

It depends on the locations of the kings relative to the pawn ( you generally want it in-front of your own pawn ), and the concept of opposition.

How can there be a win when you hit a stalemate? The players keep repeating the same cycle of moves for years until one dies of old age?

Stalemate in chess is when a player is not in check but has no legal moves that wouldn't result in a check.

So essentially it's a lost position for one player, but due to stalemate rule it will count as a draw.