> the demand for tourism to natural parks is way too large to allow unfettered access by the public

I'm not sure this is true. The United States has a huge amount of wilderness and federal land. The problem is that most people want to go to a small number of very popular places.

Allowing as many people as possible to have a nice time in nature, whether by providing facilities, informing potential visitors of their options, managing access to popular or vulnerable sites, etc, is exactly what the Bureau of Land Management are supposed to do. The fact that there is a single agency in control means that it's not really an example of the tragedy of the commons, either.