First, we have to start SOMEwhere. If you are taking off at 11,000 feet density altitude, there are a COUPLE of things you need to be thinking about, in addition to flap setting for takeoff. I'd still use 20 degrees there, however, my self.
Remember that a large part of what manufacturers recommend in their POH is somewhat modified by considerations for their own liability, while much of it is actually based on demonstrated aircraft performance. The problem comes with trying to sort one from the other.
Cessna limited flap travel to ~30 degrees in all their aircraft, recently, I believe, though I haven't flown a new 182. They did that for LIABILITY reasons on balked landings. ANY of those airplanes will not only fly level with full flaps and full power, but will actually climb. At sea Level, where all manufacturers reference performance numbers.
I've flown a number of Cessna 150s where the student almost wrecked the airplane trying to get those flaps from 40 to 30 on a go around. Take the controls and fly a go around AT 40 degrees. Granted, that would not work at 11,000 feet DA, though.
So, the point is, you have to start somewhere, and the somewhere that Cessna and every manufacturer starts is sea level. Things do change as the Density Altitude increases, no doubt, and the pilot would be wise to consider those changes. Mostly, however, the pilot needs to FLY the airplane, especially at high DA.
As to matching the aileron deflection to the flap deflection for T/O, that's a good rule of thumb, but it's certainly not sacrosanct.
Again, the early C-170's didn't even HAVE a 10 degree flap setting. So, would you suggest a high DA takeoff with NO flaps??? I wouldn't go there, myself.
As to drag at High DA: While horsepower decreases in normally aspirated engines, so does airframe drag. What we're really concerned with is the Lift/Drag relationship of the flaps, not just the additional drag. If they produce enough additional LIFT, then we can live with the additional drag.
I have very little time in C-17X airplanes with stock engines. I have a fair bit of time in ones with 180 hp or more. With a small engine, I'd still use 20 degrees for takeoff at high DA, because I want to lower the stall speed to the lowest possible, with the lowest resultant drag. If you check the stall speeds of the plane, with each notch of flaps, you'll find that 20 degrees gives you almost as low a stall speed as the 40 degree detent, but a LOT less drag. The 10 degree notch sorta slows the stall speed a bit.
At SL or high DA, I want the slowest stall speed for takeoff performance.
MTV