I can't think of another attraction in any park that has cloth seats the same way. Add people in shorts dripping in sunscreen and yeah, not the best. That's why I wear long Dad Cargo Shorts.
But, I do like the look of those older theater style seats. They should just recover the panels with new material scotch-guarded to the Nth degree. They look to be a common type in junior and high school auditoriums across the country and those are often re-upholstered.
I would imagine that's something they could get done pretty easily and cheaply with all the vendors out there that do that sort of work.