Look, it's biology, not magic. Once there is nothing left to break down inside of your beer - the yeast will stop working, that's just a simple, biological fact. Do yeast "clean-up after themselves," sure, to a certain extent they do, depending on the conditions in your beer. But that's all a part of fermentation - there's no reason why you should consider your fermentation to be complete until all activity from your yeast has ceased. So when I say that "once fermentation is complete, your yeast aren't doing anything," I'm not really saying a whole a lot other than pointing out the obvious, which is sometimes what needs to be done here in the Beginner's Forum.
Leave your beer on the yeast cake or take it off - none of it makes all that much difference from a biological standpoint once fermentation is complete. I just don't like telling beginners: "leave it on the yeast for a month, you'll get a better beer," when technically, those last two weeks didn't do anything at all because fermentation was complete and the beer was just sitting there waiting to be bottled. If we're going to help people become better brewers, it will be by telling them to gather facts (such as gravity readings) and make decisions based on facts. It's science, sure, but it's not rocket science.