Answer by Brian Dick:
The benefits of functional exercises such as push ups, pull ups, body squats, burpees, handstand push presses, etc. are:
1. They are free or virtually free. You can do them at home, at a park, or as an add-on to your standard gym workouts.
2. They are compound movements (usually the default motion, or there are variations that are) that engage more than one major muscle group in one motion. This increases the speed of the workout and their relevancy to real world applications of strength (ex., picking up and carrying your child, mowing the lawn, playing pick up sports, etc.)
3. They typically require more stabilization from stabilizer muscles than typical gym workouts (especially machine workouts, perhaps less so for free weights). This again helps major muscle groups to function more effectively and safely when engaged in non-gym actions of strength.
4. Being aware and able to control your own body weight is essential for athletic purposes where center of gravity and body awareness are mission critical (ex., wrestling, judo, jiu jitsu, football, basketball, etc, etc.) This functionality not only increases your own self awareness, but also increases a sort of “visceral” understanding of how to affect another person’s balance.