Everything in your program should be justified. You should have a specific purpose for every exercise that you do. This is especially true when you are training other people; you do not want to hurt them or waste their time and money.
Furthermore, you or your clients must be able to perform the chosen exercise properly in order for your predetermined objective to be met. If the exercise cannot be done with a certain degree of technical correctness, then why do it? You are reinforcing bad habits and risking injury without really making any improvements. Sure, you might have to work through or coach through technical disasters for big lifts like the squat, bench, deadlift, and the olympic lifts. However, you or your clients need a certain degree of functioning to do this safely and effectively.
This is not a good strategy for smaller, accessory lifts that have legitimate regressions, though. Why do jumping pull-ups with an overweight client that cannot jump or pull? If your reasoning is "metabolic conditioning", then the client needs to be able to do this exercise with a certain amount of successive velocity (I made that phrase up, but it makes sense). If they can't bounce up and down, then what is the point? There are much more effective options for both metabolic conditioning and improving vertical pulling strength that the client will actually be able to perform. Use a band and do dead-hang to chest touching the bar close-grip chin-ups. Do not bounce out of the bottom with the band, kick your legs forward, or use momentum. Be strict and make small (but legitimate) improvements over time.
Lastly, when it comes to progressions and regressions, you have to ignore the dogma and go with what gets the results you desire. If you or your clients cannot perform an exercise with a certain degree of technical correctness, then you are probably not getting much closer to your end goals. Proper exercise programming takes time and experimentation to learn. Just remember, if it looks bad and doesn't get much better, then do something that you or your clients can actually do. If you want to get someone good at chin-ups, have them do a lot of good chin-ups with a variation that mimics the eventual exercise as closely as possible. What is more alike a (proper) chin-up, a jumping pull-up or a banded close-grip chin-up from a dead-hang? Which exercise allows you to track progress more precisely? Which exercise allows you to adjust the difficulty as you get better? These are the sorts of questions that you need to ask when designing strength programs for the general population.