Archaic brewing (looking at recipes from the 1800s and earlier) often had inverse step mashing as you're describing. However, just because that's how it used to be done doesn't that's how it should be done now that we better understand the science behind it.
In theory, mashing hotter first and then cooling down would allow alpha to chop up large starches, and then beta could chop them further into highly fermentable dissacharides. However there's that denaturing problem. That said, I've had beers made by those old methods (by folks interested in historical brewing), but can't say if it did anything more than a simple single infusion at the original temp would be.
Given how most homebrewers mash (adding grains to overheated water), one could make the claim that much of the grain bed is at or likely well above denaturing temp during that initial stabilization to mash temperature, and are effectively doing this anyway. Alpha also works very, very quickly, and few mashes will fail an iodine test past the first few minutes, ie available starches are converted albeit not necessarily to a fermentable form yet. Wonder if mashing in in the upper 150s, and as soon as the temp stabilizes chilling it down to the mid upper 140s wouldn't preserve enough beta activity, and produce an especially fermentable wort by allowing alpha to do the heavy lifting first. Or, it alternatively the beta and then slows down the alpha and leaves a ridiculously unfermentable mess with poor conversion efficiency.