It is considered good practice in software debouncing not to wait until the bouncing is over, but to immediately act at the first edge because you know that the key has been pressed!
It is considered good practice in electronics to make sure that the circuit is not experiencing Impulse noise and giving a false reading. You don't know that the first edge is due to the button being pushed: Instead, you should recheck a short time later to see if the input is still high.