Automated stirring is supposed to keep the grain in suspension and even out the temperature of the grain bed. I don't use one, so I can't say whether or not it's worth the trouble. I prefer to do a continuous recirculation with a pump.
"Just having the HLT heating should create a cycle between hot water rising and cold water falling."
I can tell you from experience that this doesn't work as the thickness of the mash inhibits convection currents in the mash. There is surely some convection circulation going on, but it's nowhere near enough to keep up with the heat applied. The result is uneven heating with the lower portions typically overheating while the upper levels cool excessively. IIRC, at least some of the commercial breweries stir the mash continuously, but I don't know if they all do it that way. The common home brewing HERMS and RIMS systems circulate the wort through the mash primarily to even out the temperatures. A lot of the mechanics of brewing seem like they would be no problem until you try to actually implement them. You would think that something like a false bottom would be virtually fool proof, but they are not. Same with heating up the mash. It's not as easy and straightforward as you might think. This is also why you see so few identical systems. There's no single perfect way to brew and that goes double for home brewing.
My off the wall and eccentric concept would be to have the mash in something like a small rotating drum similar to what a concrete mixer uses. At the end of the mash it would go through a spin cycle like a washing machine and extract the wort by centrifugal force. The problem is that this would be unnecessarily complex, expensive to build and difficult to heat. The mind is a playground. I go there a lot!
Oops. Never mind. I thought he was talking about the MT, not the HLT. Actually though, a stirrer is useful in the HLT with a HERMS. The heated water will cool immediately adjacent to the HERMS coil and the heat transfer will slow dramatically. It needs to be stirred to work efficiently. Heating alone won't do it very well at all.
