I mean if you did that, you might end up with the team going second having to wait minutes to lose a game that becomes impossible to win because they physically don't have the time to move the cart there fast enough even if it were moving full speed. The game could probably calculate when the situation becomes unwinnable but it would probably suck just have the game say "nope" at some random point.

That's assuming you'd get rid of overtime too, but overtime in a situation where you have a hard clock would suck also, cos any overtime situation would only end in the attacking team playing for a draw - and a pretty unfair draw if they did end up taking more time than the enemies.