The "rent vs buy" math is often more about convenience and options than it is about saving money.
In this case, the argument for buying would be the ability to install improvements - concrete piers, a real building (with septic, water tank), solar panels and batteries, etc. Of course those would require additional investment, and without frequent supervision could be destroyed by vandals.
All that said, I only get down to LSA a few times a year at best, so I'm with you - supporting the park is the clear choice for me.
Mark