Truth is, I have stayed at a public campsite within a public park. I agree, the site was too crowded from my point of view. How about this for a solution. You have tiered pricing in the park. Zero price gets you into the crowded, but free, part of the park. If that's not what you like, pay a higher fee and you get into a less crowded part of the park. By having several tiers, you can let the consumer decide how much privacy they are willing to have. Tiered pricing is done all the time (e.g., music concerts), so why not let the consumer decide how much peace and quiet they want? The way it is now, you don't have a choice. The current system of one price buys whatever the status quo is for the park on that day. And most of the time, that isn't what you'd choose to have.
Free (plus the price a decent 4x4) buys you access to a reasonably secluded logging road with toilet facilities consisting of an entrenchment tool with a roll of TP on the the handle. (Useful test for girlfriends, High maintenance girls should be left in town.)
The forest service is largely irrelevant to wheelers. We open trails faster than they close them. Once again 'the law is an ass'.