I think PETA has a bigger issue with bowhunting than rifle hunting. And just because something is not allowed for hunting does not mean it's illegal to own or shoot recreationally. The logical conclusion of rifle hunting with no limitations is that rifle hunting becomes shooting, and the number of tags available will be equal to the number of animals the biologists want killed.
Conversely, by increasing difficulty, we can support more hunters and, consequently, will have more people to defend hunting, guns rights, etc. If hunting becomes a thing you get to do once every 5 or 10 years, a lot of people will just throw in the towel and no longer advocate for these things.