Many dishwashers do operate off a timed fill, but typically have a float for overfill protection. Of course a float doesn't help if the water valve hangs open.
A few (like KA for some years), have a pressure switch for overfill. Our KDI-17 had a pressure switch (and dual-water valves for backup protection against valve failure). I'd sometimes reset the timer for maximum fill. Once the pressure switch activated it wouldn't fill any more even by resetting the timer. However, when the max level was reached, if the cycle was paused and restarted, there'd be some leaking for a few moments from the door vent upon the restart.
My KUDS-22 has a float.
I'm not sure what DishDrawers do for overfill sensing. The fill may be timed, but also is sensed by feedback on the motor. DishDrawers also have a flood sensor in the bottom floor of the machine.