Increasing prices will increase equity. By charging rich people more, you can afford to give greater subsidies for marginalized groups and poor people, and lower the price from whatever it is currently for them. You can even use that revenue to pay them to go camping, if you really want to!
In any event, that unlikely to be helpful in this specific situation, as the majority of all revenues from rec.gov go directly to BAH[1], rather than to the public land management agencies responsible for stewarding the resources in the public interest.
BAH also has price setting authority, with a dearth of public oversight.