I'm sure there would be an uproar. The numbers are not undergoing any rapid changes. The reason is all these PETA type lunatics. They see a cute animal, and hear that somebody shot it, so they just commit and go gangbusters on the issue. Sport shooting does not affect prairie dog population at all.
Poisoning is the only way to damage their numbers.
People poisoned them a long time ago, because our whole continent was one big dog town, and that is a bit excessive. There were way too many dogs. Right now, the prairie poodles occupy an acceptable range. The prairie dog is not endangered. Loose talk of banning shooting and other methods of control have caused more poisoning to happen.