Actually, my impression is that there are plenty of Wats in Thailand where you could stay and set your own schedule. I did that a couple of years ago in the Bangkok Wat that my local Wat is a "branch" of.
The main problem is language. Outside of tourist areas English just isn't an option in most cases, so it's non-trivial to set up a visit. And, of course, the places that are set up with organised retreats will obviously have organised rules...