Most of our large National Parks are located in rural states with a low tax base. The single largest expenditure for those rural states is education. After that its programs like SCHIP, and various safety-net type programs, then infrastructure, after that its policing and emergency services. Parks, DNR, state forests and so on are way down the list and are the first to be cut when the state gets into budget trouble. For example, Wyoming simply does not have the tax base to manage the National Parks and Forests located within that state without selling much of those parks and forests off to developers. So unless you want Yellowstone to become another Vail, leave it in the National Park System.
National Parks are a tiny fraction of our federal budget outlays, if they have issues, then fund them a little better. Why mess with this nation's single greatest idea? Our National Parks, Forests, and Federal Wilderness Areas are literally what makes this nation unique. You can strap a pack on and completely leave civilization here and experience true freedom as long as you are out there, there are few other places on earth that you can do that in.