I agree about being cautious about using this. It seems like a good way for new people to mess up their shoulders. The thought of hitting crimps that hard/fast is terrifying.
I do really want to take some of my friends who climb like Fred Nicole (super slow and static as possible) and make them use this though. Sometimes utilizing momentum is important. Sometimes climbing everything static is a huge waste of energy and is actually bad technique, despite being generally safer and better for training outright strength (as opposed to power).
Oh it's already a thing, injury or no.
The parent is worried about the combination of pushing the limit of what you can do safely with your strength and doing so as fast as possible. This can lead to being out of control, and strength and technique are part of what keep you safe.
You should probably have a very high level of climbing fitness before you even consider this, though I can see it being potentially quite useful. You would also have to break down what is going on in the route that is generated and how it might be dangerous. Throwing out drop knees[0] and heel hooks[1] and yanking on crimps[2] is a great way to get wrecked if you don't know _exactly_ what you're doing.
[0] - https://www.youtube.com/watch?v=KHlzC7EqyDA
[1] - https://climbingtogetherandotherfunadventures.files.wordpres...
[2] - really tiny holds => https://www.google.com/search?q=climbing+crimp&tbm=isch
Time trials sound like a quick avenue to painful injury, though. If I were a gym, I'd be cautious in encouraging it. In my experience, climbing prowess is not a matter of speed but control -- the more statically you can complete a route the more control you demonstrate. A friend of mine once said his goal is to complete a route as silently as possible, avoiding accidental scuffs of his shoes or knocking of his knuckles on the wall. This is actually a great measure of control, too.