Why don't short runways use (downhill) ramps for takeoff?
it could always back-taxi on the runway before turning around and taking off.


So ... that would limit the steepness of the slope significantly, and thus the potential benefit.

Most other aspects are already covered by Bjelleklang's answer: Landing aircraft would either have to clear the obstacle before being able to touch down, or they'd fall over the edge if they don't brake in time (rather than, as these days, get stuck in the grass behind the runway end)