Now that that's out of the way, are there any good (ie technical) reasons why this is a dumb idea?
Well, I guess what I was saying wasn't clear. here's what I was getting at: http://beerbarons.org/pdf/brewingCheatSheets/mashRests.pdf
(temp range / optimum)
Beta Amylase: 52-68/60-65 C - fementable sugars
Alpha Amylase 54.5-77/68-70 C - dextrins, long chain sugars
So if you have one mash at 52*C you'll pretty much only get beta activity (let's ignore the proteinases for now). If you have another mash at 70*C you'll pretty much only get Alpha activity. Temperatures between these ranges will have different enzymatic activity proportional to how far from optimum the mash temp is.
Alpha and Beta are complementary enzymes. They need each other to produce a proper wort. Think of it like making firewood. Alpha cuts down the tree, Beta cuts the tree up into logs. One won't work without the other.
Separating the mash into two mash at different temperatures could make one mash highly fermentable and one mash highly unfermentable, but you could get the exact same ratios of alpha and beta activity in a single mash.
(EDIT: now that I wrote that, I remembered a highly fermentable "reverse" mash schedule where the mash it taken to 160*F and slowly backed down to 140*F to get a highly fermentable wort. So I don't think just mashing below alpha range would actually make a fermentable wort)
The only time I could see doing two mashes would be when using, say undermodified wheat malt and overmodified British malt (Maris Otter/Golden Promise), where the wheat malt needs some protein/beta glucan work, but the proteins in the rest of the grain bill would be too degraded by extended low temp rests.