Lifting your hands off the floor at the bottom of a Pushup is effectively a way of making sure that you complete every repetition equally and with the same full range of motion. By doing this your form is more likely to be consistent, meaning that you’ll get more from the exercise.
It’s also a more difficult movement which means that you’re going through the full range of motion with the targeted muscles, which makes for a better stimulus for muscle strength and growth.
We don’t train because it’s easy right!?