I can't imagine Lake Titicaca not being inscribed one day though it will be interesting to see which parts make the cut. So many culturally and historically significant areas are being altered and modernized by mass tourism that I worry it might be lowering their chances of actually getting it done.
While I generally agree that the tourist parts of the lake on the Bolivian side (Copacabana, Isla del Sol) are nicer than the touristy parts on the Peru side (Puno, Uros, etc) we were glad that after a brief debate over skipping it entirely we decided to give Peru's side ac hance. Puno is unpleasant and so many areas smelled like urine it was very offputting. Don't bother staying long and don't bother with the tours. By far the nicest area we found on the lake was in the Capachica peninsula at the village of Llachon. The is beginner's DIY. There are minibuses that go direct to Llachon from Puno (saving you from the longer boat trip that is also possible) and a handful of affordable family run guesthouses that provide food too. If you want an authentic village experience, freedom to wander and explore the hills with some excellent views this is the place. We saw a few other visitors but for the most part this is still somehow "undiscovered" by the backpacker and package tourist crowds. The only thing it was missing were the significant ruins you'd find around other parts of the lake.