The mindless job of dishwashing is just another way to think about a problem away from a computer, plus it's useful.This works if your coworkers are happy to leave you alone to think. I often pace the halls at work while I think, but the moment I step into the breakroom I get greeted with "Hi Michael how are you so nice to see you how was your weekend" which makes the exercise kind of pointless.
Not that I have anything necessarily against small talk, but the time spent in the breakroom is unproductive time.