Preface: This relate to cupcakes, too. Also, by "casing," I'm referring to the paper wrapper that surrounds the base of the muffin and/or cupcake. For example, this is the one I use. Lastly, there is plenty of info out there of how to avoid casing coupling to the baked product - this question is not about that.
Anytime I bake muffins with casings, they stick (and eventually rip of surficial parts of the base, which isn't grand). To mitigate this issue, I've noticed that the following (presumably very unconventional) workflow results in muffin casings cleanly detaching (or not sticking) to the baked product. Regardless of the fat or sugar concentration, this consistently works well. This workflow (to me) isn't really practical, but I'm curious to understand how it actually works.
After baking and letting the muffins sit on cooling racks (20-30 minutes), I then put them into (tied) bags and let them sit in relatively warm (80-90F), humid environment (RH, 60-80%) for 2-3 hours. Of course, residual heat from the muffins result in condensation within the bag, which slightly moistens the muffin crumb. For the muffins that I try to remove the casings right after or during cooling, sticking and ripping (some or a lot) occurs. However, for those that undergo this long, odd process, the wrappers cleanly, easily detach, and I'm profoundly confused by that.