I have been with multiple barns (each teaching a different stage of riding: one the basics, the second how to be safe and confident at around 1m, and the third going up into higher classes) and not one allowed jumping without a trainer in a lesson for safety and some liability issues.
My trainers do not let clients jump without them and they all have worked with HIGHLY classified and well know trainers who show at FEI levels. I believe it is mainly out of liability and safety.
As in the trainer's horses or the client's horse? If the latter, then I can't see why they would stop them. The client has to jump on their own at some stage and develop their own sense of awareness. I wouldn't think they're a good trainer if they have to micromanage everything, unless the rider is novice.
If it's the former, I can see why they'd be hesitant but again, the client will have to learn to develop their own sense of awareness at some stage too.