I'm currently at 16, with 12 scheduled over the course of 4 weeks. I've heard it's wishful thinking too, but I'm stubborn enough to try it anyway. I just feel like it's really important to find the best fit for the next 4-5 years, and thus I can stay motivated, especially since I like all the places I'm scheduled to visit. Of course, at some point it just becomes logistically non-feasible.
My only advice is to schedule maybe one or two "practice runs" at the beginning that aren't your top choices, then schedule your top choices immediately afterward while you're still fresh. Although you don't want to cancel any interviews, the best thing you can do is schedule the ones you'll regret canceling the least at times when you're most likely to feel the burnout.