Hello there, I am of the not-so-informed opinion that rim brakes are fine

They certainly have been fine for me, both on some pretty steep downhills and for a _very_ rainy 8-hour ride (100-miler in typhoon Japan weather LOL). But as to your question:
"I was worried about heating my rim and blowing off my tire. Has that ever happened to anyone?" I was recently in a GranFondo, and there was this guy right in front of me with carbon wheels going downhill on a pretty steep incline. There was a safety motorcycle escorting us (there had been an accident ahead), so we had to keep constantly on the brakes. Unfortunately for the carbon-wheel guy, his rear tire blew up
If I ever switch to carbon wheels (unlikely, though it's just a personal preference), I would also switch to disc brakes for this reason alone. I read on this site that rim brakes on carbon rims can lead to this very situation easier than with aluminum rims.
For what it's worth
Geoff