Responsible recreation is what gets people involved. Without people going "Cool, this needs to be protected" you get a bunch (NOT ALL) of people who have no real experience. While you can be taught what a car is & HOW to drive it in a classroom, untill you have real seat of the pants wheel time you are clueless. If you only drive under ideal conditions in a controlled enviroment you haven't a clue as to handling, performance or economy. Recreational cavers (responsible ones) are needed as they often see a far bigger picture in a cave than someone who doesn't love them and is only looking for one thing or one thing at a time and only on a limited basis.
Would I pay a fee? It's a slippery slope but maybe....if I knew it was a worthwhile cave and there would not be Jerkus Americanous being stupid messing things up for all eternity.....and there weren't too many power trip rules that made little or no sense in the real world...Also what would the limits be? One trip a year? Two? By reservation and only one in at a time?
Not enough info to give a firm answer.
My definition of a recreational caver might not be the same as yours, most of my friends are recreational cavers, no "Degree", we help with conservation, restoration, help with scientific projects. ...then there are short timers who lose interest quickly and move on to the next thing and there are occasional cavers, those who only go once in a while as opposed to every chance they get. And of coarse there are spelunkers....not even going to go there