I've never used lift the toes. I don't do it either. And you don't flex a ski boot by lifting your toes. If you do, the boot is way too soft. Like hiking boot soft.
All this small muscle talk on this one being better than large I think is probably nonsense, but I don't know enough to say. I suspect though that the use of the "small muscles" to lift your toes locks up all sorts of things and screws with your balance system. The foot to ground relationship is important. Tensioning the arch of the foot is key. I think lifting the toes screws with that.
I've never gotten this instruction and judging by vindibonna1's daughter it can do more harm than good. I'd more use wiggle toes to get people to relax and stop clenching their toes. You tell people to lift their toes, and quite possibly all the fear goes in there and locks up the whole ankle.
But hey, use it if it works. I've never skied that way. I don't doubt I do it at times but I almost never think "lift my toes". Except on the lift trying to warm my feet. Lifting the foot - toes to knees, and relaxing, say 100 reps can warm the feet. Well at least it's supposed to. It does warm up the shin and distract oneself from the cold feet.
"Lift the toes" = Old wives tale
"sit back in powder" = NO, but sometimes ya got to