Bodyweight exercises allow you to adjust difficulty in infinitesimally small increments by altering body position to increase or decrease torque, and they minimize the chance of injury by eliminating external load which could cause injury if out of control. They also increase coordination relative to machines or free weights with benches. This is the case because one most learn new positions to advance and access more demanding bodyweight exercises, while free weights or machines allow difficulty to be adjusted via increased external resistance.
If you think you're too strong for bodyweight exercises complete the following:
one-arm legs together push-up
one leg glute ham raise
one leg squat (with back straight and upright, and working knee behind toe)
These are tough but if they're too easy I can prescribe way tougher.