It depends on what you’re or the client is looking to gain. I have seen progressive muscle stimulation using body weight exercises. I often use a lot of body weight exercises, changing the modality as the client progresses. For instance: push ups: change hand placements, up/down, incline, decline, on a stability ball, walking, etc
Almost all body weight exercises can be changed in this manner changing which muscle fibers are continually recruited, increasing/decreasing the intensity of the exercise and keeping it interesting for the clients.
Jocelyn has some very good points. You could also increase the number of repetitions, do the movements slower, combine 2 or more exercises to increase the intensity and the variety (for example do pull-ups/pushups/bear crawls/dips all in the same set or mix jump squats/lunges for lower body) and in some cases put on a backpack to make it more interesting. Also changing the surface where you are doing you exercises can have an impact (for example hard floor or cement vs. sand). Most of the exercises can be done by going uphill or downhill as well.
There are countless ways in which you can perform body weight exercises in order to make them more difficult and more fun.
Depends on starting level and what you consider strength. If I did bodyweight only all of my lifts would go down, but my squat, deadlift, and good morning are all over 400lbs. There wouldn’t be enough of a stimulation for me, but for some people squatting the bar is difficult and double leg body weight squats progressed to single leg squats would be enough.