Some of those aspects of park operations have already been contracted out to a significant extent
https://www.wsj.com/articles/national-park-fees-booz-allen-6...
https://www.thebignewsletter.com/p/why-is-booz-allen-renting...
Edit: And this also totally misses the point of the parks to begin with. They're there not just to entertain visitors but to preserve these landscapes for posterity. Privatizing them would totally go against that. We don't need anymore land barons exploiting the masses and preventing them from experiencing the places they have a birthright to.
Having been to the Canadian ones, it is quite easy to see extremely well managed private businesses in parks. I didn't have a single poor experience (compared to the US ones).
Of course, making management of the whole park private? No way.
These parks are our nation's shared treasures, they should just be free like the D.C. museums. The last thing they need is more privatization. The NPS does a fine job at providing the visitor services that AREN'T totally commercialized (rangers, upkeep, lotteries, etc.)