Because check mate is a very small subset of possible moves at the end game, I'm guessing the vast majority of games will end(?) with 2 kings moving around randomly for all of time. This assumes most games will make it past the hump of mid game where its possible the king's motion will be limited and a checkmate can erroneously happen, I suspect this is a rare case as well. On a side note I wonder what kind of useful…
edit: forgot you can checkmate with just a king and a queen