It's that old respect thing again then. If people are going there with a respectful attitude, they could probably hold a full-on party, but leave no litter or damage.
But then you get (probably well intentioned) folk who just don't think (or who just don't care) about the effects their actions may have. If it's 'cause they don't think, then info may do the trick, if they don't care, then only barring access would work. Shades of the recent talk about climbers on the Lamgdale Boulders.

I just hope it isn't an excuse to put a gate on and charge for access in the future. Cynic that I am.