Booking ahead compared to Hueco isn't comparable as I don't think you can actually stay in Hueco - whereas you can in the Peak. So a family camping in the Peak would have to pre-book all their car parks for the week, which is just impractical.
Another issue with parking vs public transport is for a group/family of 4, looking at current transport prices, it's cheaper to drive and park than buy 4x train tickets, and much more convenient too.
So public transport would need to be subsidised, and suspect car parks too.
That £4.75 cash-only charge is just ridiculous. It's 2021.