I get the sense that this is possible, but from what I can tell, the yield doesn't justify the time/effort involved. Not to mention the raised eyebrows at the post office or bank.

Perhaps my opinion would be different if I lived or worked in a building that had both a post office and my bank in the lobby. For me, this strategy would involve a lot of driving and waiting in lines. I always thirst for FF miles, but not that much.