7 years later, Sun Microsystems cofounder Vinod Khosla loses bid to privatize public beach

I confess your question puzzles me, since there is no easement. If Surfrider or someone else were to purchase an easement, then it would allow whatever its terms specify (And would almost certainly include the right to park cars.)

But no access easement exists, since only unpermitted access creates involuntary access easements. Access given by explicit permission of the owner creates no easement, and the car-park fee is an explicit permit.

Permitted access can be revoked at any time at the property owners’ whim.

It’s only when there’s a history of continuous use without explicit permission that the “involuntary easement” provisions kick in.