They do (but this is different from a suicide break). I'd say most people use the pedal for breaking, the exception are mostly people who are a bit older and benefit a lot from gears, and somewhat wealthier people (as the pedal break bikes are usually a bit cheaper and often second hand), but even then I'd say I still see most people wearing suits who cycle, cycle on pedal break bikes.

"Coaster brake" is probably the more common term for this setup. It makes for a more complicated rear hub, but works better than calipers in rain and snow and gunk.

It's common, and I like them a lot.