No, it's not a dumb idea. However, I think you are missing the difference between a starter and the primary fermentation.
You pitch a starter to make more yeast. You don't really care what becomes of the wort, so you ferment at room temperature and try to get things done quickly. As long as you wind up with a bunch of yeast.
You pitch a primary to make beer. You care quite a bit what happens to the wort, so you control temperatures and manipulate the fermentation in other ways. You aren't as concerned with time as you are quality, and you aren't concerned with maximizing yeast production.
If you were to put a stirring plate in the primary, you might get a faster fermentation and a larger yeast cake. However, I don't know what you would get for beer. It seems like the best case scenario would be that you get no better quality. Even when you get a stuck fermentation, a single, simple rouse usually gets it going again.