I was sitting pondering deep thoughts and found myself wondering what drives the overwhelming preference for wort recirculation by pumps over a direct agitation of the wort during mashing?
Or put another way, why are there no homebrew scale automated mash rakes?
Because it’s overkill? Because recirculation is easier and less expensive?
I’m guessing heat loss is the reason. Besides being unnecessary; but then again I don’t pump anything for that reason as well. Stir the mash at the start and then I let it sit. It works.
I can understand the argument for doing neither (my current approach).
But if one has decided to complicate things by doing something to keep the wort mixed up … my current hypothesis is that pumps are preferred because they are (at least theoretically) multitaskers (a lot of three-vessel systems include a pump or two for transfers); whereas a mash-stirrer would be a unitasker. Also, if you’re sparging, your initial water/grist mix might be thick enough to challenge cheap home-scale electric motors — but this needn’t be an issue for no-sparge approaches.
My inner contrarian kind of wants to find a way to try it just because no sane person does it that way. 
I recirculate with a pump because I have a pump. (I recirculate throughout the entire mash.)
To install a rake I’d have to add another component to the brewery which I don’t want to do. Just something else to clean.
I did see a guy on YouTube that attached a motor that ran a paddle. Funny thing is they don’t show the thing actually stirring the mash:
I actually built a motorized mash stirring system using a whirlpool paddle like shown here:
I started with a battery-powered electric screwdriver but it wasn’t designed to run steadily for long periods of time and the batteries didn’t last. I bought a motor and made a mounting system with sheets of acrylic and pvc tubing posts. Adapting the motor shaft to the stirrer shaft in an easily removable manner was a challenge, but it was cheaper than a pump. I used it for stirring during the mash and also when chilling with an immersion chiller. It was a pain because I had to lift the whole assembly out after the mash and put it back after the immersion chiller was in place. It was tall and awkward to lift and was difficult to take apart. I eventually switched to a pump and am much happier with that. It is smaller and quieter and it doesn’t interfere with getting the immersion chiller in and out. No standing on a step ladder to get the paddle out of the kettle. The only downside, besides the cost, was the hit to my reputation for building things myself.
Maybe my experience doesn’t match that of others. I have recirc systems in both a HERMS for 10 gallon batches and an Anvil recirc for 5 gallon batches, but I don’t think I have recirculated in over 8 months…I just went back to stirring the mash several times through the course of a mash, applying low heat (50% power at the set point) on the Anvil and no heat on the 10 gallon batch (the mass seems to hold well enough in my InfuSSion Mash Tun). Easy peasy and a little less to clean.
I can see the desire to mechanize, but more and more, I return to simple approaches used over the years (like batch sparging!)
If recirc wasn’t so easy on my system, I’d be right there with ya.
I forget sometimes that my setup is just ½ or even ⅓ the volume of a lot of folks’. What’s feasible or convenient for 6-10 L may not scale to 20 or 40 L. Nothing I do remotely approaches requiring a step ladder.
I quit sparging altogether. Mash in, recirculate, lauter, boil.
Disclaimer: Any comment I add is simply the way I brew beer. There are certainly other ways that can be equally effective which other brewers may contribute. This is what I’ve found that works for me using my equipment and processes so I offer this for your consideration. YMMV