You get much nicer parks if you turn them into profit centers rather than a drain on the state budget. That's pretty much all there is to it.
This guy has a business that manages public parks, and he will have some blog posts on why it makes sense and what people misunderstand about the process. That's obviously self interested commentary but it seems pretty evenhanded.
https://coyoteblog.com/ He links to this from his site:
http://www.parkppp.com/ Not sure if that is his site or a trade group.
One big thing that privatization gets you is you don't have to put a PERS load on every full time employee, so it's much cheaper. And I think it's easier for private companies to utilize part time and seasonal labor. In fact, I think he has said on his blog that the majority of his workforce is part time retirees. They get to enjoy being around people and go where the weather is nice and supplement their income while essentially living in a park they would want to visit anyway.
The other thing is that if you give a private company a long enough contract, they can make investments in the park knowing they will manage it for a return and not manage it for political concerns. And they can just make investments in the most cost effective way. Since it's their money, they don't have to promise to figure out a way to give the work to whatever legislators son-in-law in order to get funding.
We've got several state parks that are limping around that have pretty good assets. Hugh White, Enid, Sardis, and Bucaneer state park all have pretty good set ups and I think Buccaneer is the only one that turns a profit for the state. Don't know what kind of shape it's in now, but Hugh White used to have a really good golf course. Not as good as it should have been, but a really good set up that would be very desirable if they kept it up. May not be a populous enough area to put the money into maintaining it, but if there were nicer cabins, that would be a pretty decent weekend trip for people. But you'd have to get over the political problem of charging a nice green fee for a nice course.