NFL

The center and QB still have to complete the snap successfully though so I'm not sure what good this accomplishes.

Provided the QB established possession. But what are you really saving in that fraction of a second it takes to kneel down? You aren’t saving more than a single second of time.

Besides the holder I rarely see it in a player. The refs on the other hand are on their knees some plays, mainly when they're blowing the game.

Didn’t a kick returner lay flat in the end zone then stand up get the ball and make a decent return? Vikings I think?

Obviously different than a snap, but player starting the play down.

A QB taking a snap on his knees would be much harder than if he's standing. He would have to hold his hands funny. It would lead to more fumbles than less.