Perhaps, just perhaps there are environmental cues that we haven't yet figured out, which signal to a fish that growing larger isn't going to be a good investment of it's energy. Now I agree that poor water quality, injury, and illness are probably among those environmental cues, and possibly the more common ones seen in an aquarium, but are they necessarily the only cues? I don't pretend to know what could make a healthy fish stop growing, but I have seen ponds and lakes with seemingly healthy sunfish that are stunted. We did age and length measurements on sunfish from such a lake in a biology class in college. Examined scales under a microscope to get the age. Then we plotted growth rates. They grew about an inch a year for about 3 years then dramatically slowed down topping off at about ~4 to 5 inches. These fish were not emaciated, and they appeared healthy, they just weren't getting big (well okay they were dead so didn't actually appear healthy while we were removing scales,

I don't know if paddlefish specifically can be kept small and healthy, but if they were otherwise going to the garbage I guess I don't see the harm in trying. The worst that will happen is the paddlefish will get to live a few extra months/years, before outgrowing the tank and dying, and the person who bought it will learn the hard way that large fish can and do outgrow small tanks.
I myself have no desire to try and keep a fish as a pet that I know will get too big for its tank and will have to be killed. I don't see it as a problem though if others do. As and example if I can go fishing today and bring home a bluegill for the frying pan tonight, what's the difference if someone else goes fishing today keeps their bluegill in a 20 gallon aquarium for 6 months and then kills it when it gets too big?