I understand the need to keep adding resistance, though as my sibling commenter says, I think you're understating the potential of pure bodyweight progressions to increase strength. Exercises like one arm push ups, one arm chin ups, hand stand push ups, planches, pistol squats, nordic curls, etc. can be equivalent to seriously heavy weights and there are plenty of options for gradually progressing toward them. Lots of muscle bound guys who can lift a lot of weight still aren't strong enough do any of these advanced bodyweight moves.

But anyway, what does that have to do with comparing burpees to squats/push ups? :)

Not fully true, body weight can make you gain lots of muscle, but you do need to add resistance. However, resistance doesn’t need to be weight or bands, but do a more difficult version of the exercise. Push ups are easy for you? Do planche pushups or diamond pushups.

Squats easy for you? Try pistol squats.