You end up with a situation where the wealthy can do everything and the poor can do nothing.
And then there's the super rich, who could buy out the possibility of anyone else participating, literally turning such places into their private playground for eternity if they so wished.
Like, what price could you price it at where:
1. You could afford to go occassionally
2. Elon Musk couldn't just buy out every single ticket for the next decade to make it their personal playground.
There's simply no feasible solution to that.
Just auctioning everything and letting capitalism take its course just denies a vast segment of society from participating at all for activities where demand outstrips supply.
Supply & Demand only works if supply can be increased, so that as prices rise there's incentive for greater supply.
For things like National Parks or Taylor Swift concerts, price discovery through "supply and demand" does not work because supply can't increase to match supply no matter the price.