I once saw a guy descend the steepest, long hill in SF while doing a wheelie.

He rode a coaster-braked old 26" Schwinn, and when he got 2/3 of the way down, the hub began billowing heavy smoke, which of course was his intended show.

The brake didn't fail, though I failed to note if a 2nd brake was in place (likely not).

Some coaster bakes compress an alternating stack of inner-tab/outer-tab brake disks, and this stack is somewhat thermally isolated from heat escape through the hubshell.

Most good coaster brakes have shoes rubbing against the inside of the hubshell itself, so there's some escape path for heat buildup. These also can fade.

My brother and I were riding along one of Washington state's rail trails on my Aunt/Uncle's cruisers, and I had my chain fall off as I began braking for a road crossing.
I was able to drag feet to a stop and re-install the chain. The chain wasn't very tight as I recall, and these were little-used inexpensive bikes.

Coaster brakes and lever-op hub brakes tend to be very non-linear, i.e. grabby, during emergency-type stops, so not half as good as a decent caliper brake in these situations.
Having to swerve sharply also makes any coaster brake a poor choice for that situation, since the foot positioning might not be at all favorable.