Good discussion here!
I can speculate that a good stir moves the sugars into the water; the same thing happens with recirculation, although the edges of the grain bed in the malt pipe are likely under-washed while the center may be over-washed. If there is such a thing.
I also can believe that at the start of the mash the grain temperature is mostly even and correct (assuming a reasonable strike calculation), but I strongly feed this changes rather quickly. Maybe I am a fanatic for wanting to be within a degree or two with my mash temperatures? That's why I recirculate - even and consistent temperatures.
So, mash-out: I sparge at 170F, and that's my mash-out. The folks at the FLHBS suggested that I just add some grain and forget the sparge, but I use the sparge to adjust the pre-boil water volume to be where I need it. In my Brewzilla, 6.5 gallons is too much water, it really wants to overflow, so I always (try to) start with 6.25 gallons. My recipes typically use 12-13.5 pounds of grain, and this can be recirculated at a reasonably high rate without fear. I want 5.5 gallons into the fermentor, so I can keg 5 gallons.
My efficiency numbers are good, sometimes higher than expected. So I am not missing much in the way of fermentables, and I'm satisfied with the gravities I'm seeing.
All that being said, I think I have some new techniques to try next brew:
1. Stir the mash at 20 and 40 minutes to allow the edges of the grain bed to better participate in releasing the goodness of the grain.
2. Wait 10 minutes or so to start recirculating. OR at least, get a better temperature probe to measure what the center of the grain bed is doing, instead of just measuring the recirculation water at the top.
3. Try a mash-out (trivial with the brewzilla) by bumping up the temperature by 15 degrees F or so, give it 15 minutes to try to heat up that much. (I can 'pulse' the big heater element, 30 sec on, 30 off, to avoid burning the wort - that has a big effect).
4. Pay closer attention to efficiencies. Not for economic reasons, but to gauge my brew process effectiveness. (In the last 4 brews, the gravity was higher than what the recipe said; my equipment profile assumes 75% brewhouse efficiency).
This is the stuff that makes this so damned interesting. Besides the beer, of course...