Rationale behind a stalemate
For friendly games, you can play by whatever rules you like (or if you just don't know any better). When I first played chess with my son, we didn't know what to do about stalemates and situations where we didn't want to make a move, so we implemented something like wiechi/weiqi where a player can "pass" on his turn; if both players pass consecutively, the game ends. It made for pretty interesting games.
Give it a try.
Why is it not the case that a player having a king with no escape squares, but not in check, does not lose on time? I understand completely how insufficient material and repetition lead to stalemate. With insufficient material, no mate is possible, and with repetition the players are essentially agreeing to a draw (or at least they should do so, rationally). But if the enemy king is stuck, isn't the opponent just deciding not to move into checkmate?
I'm not suggesting we change the rules, just curious if there is some reasoning behind this I am not aware of.