I think it would be almost crazy for a private entity to take on something as large as a national park. Imagine the liability that they would be assuming. What would their insurance costs be? Probably cost prohibitive. I also envision very strict governmental regulations on what they could do with the park and it's resources. That would add more overhead to ensure that the park was in compliance with all the bureaucratic hoops that were put into place.

I'm no business expert, but I think that the captial required to operate something as large as a national park would make the user fees prohibitively high, which would keep the public away unless there was something unique that would draw them to the park. Do the user fees we pay in our parks cover the expenses of maintenance? I doubt it.