With the dire situation our country is in (please don't let this digress into a political discussion), and in light of the treasure our National Parks represent to current and future generations, I'd be more than happy to chip in for my use of the Park's resources, if it helps to ensure its preservation.
I agree with the above, that reform to the way the backcountry is regulated might be in order, though with the ignorance that seems to run rampant among even backcountry campers with regard to LNT and general etiquette I'm not sure changing the current regs that forbid stealth camping outside regulated campsites would be beneficial. The current sites ARE heavily impacted, but that seems to help preserve 99% of the land at the expense of the 1%.
Current rules generally don't stop those who know what they're doing from stealth camping, but generally keeps those who don't from doing so. Seems like a decent situation to me.
Bottom line, charging could reduce volume of campers, raise a little bit of needed revenue, and even help support/improve the park's conditions. If the prices are reasonable, I'm for it.