At the treasurer's office in my tiny little county, they no longer needs to take checks to the bank, the bank gave them a scanner, they can sit at their desks and deposit the checks. Then the checks get mailed somewhere to get returned to their owners. Surely if a small county such as mine (less than 35k residents) has access to such a marvel of technology, the federal government does too.
Paying ahead through recreation.gov would be nice, and I think the USDA is making progress there... I see several rustic USFS campgrounds near me are on the website now. But paying ahead requires planning ahead, and sometimes its more fun to just go about without a plan.
I concede that I'll carry some small change cash in the camper for paying the fees if the situation looks good, if not, I'm sorry Uncle Sam, but here's a check.