the total distance to get "off" the ground is not reduced by the soft field or short field takeoff methods, compared to a straight max performance takeoff where you rotate at the lowest flying speed and go straight up
I'm not in agreement with this. Though the PA 28 is not the best type differences for showing the differences, failure to use the appropriate technique on other types will result in performance must less good that the POH presents.
The reselection of flaps during the takeoff roll, though done, and sometimes quite effective, is not a technique you're going to see in a POH, simply due the the risk vs benefit.
With a soft field technique, there is the presumption, that the ground run portion of the takeoff is the only distance you're trying to minimize. You're expecting to get airborne in ground effect, and stay there for a while.
It is my opinion that in general, the manufacturers simply don't want the liability of the risk that pilots will crash while experimenting with even shorter/softer field techniques. Even the amazing deHavilland Twin Otter is capable of much shorter ground rolls than the POH says, but the risks of getting it wrong are very high, so deHavilland won't tell you how. (one of their test pilots taught me though
).
I am happy to think that other than takeoffs with high crosswinds, or granny and the aunt aboard, every pilot would purposefully practice either short or soft technique on most of their takeoffs, as Thing obviously has, It will make one a much more confident pilot. Many times I've had an air traffic controller (some have more time and are more bored in parts of Canada) ask me if an aircraft was STOL equipped based upon watching my takeoff or landing (no screaching of brakes or anything, just precise flying). "No", I'd reply, just practicing...
As for the application of full power on the brakes, yes most POH's say this, but I never do, unless it's a fliight test. Paticularly with fixed pitch props, the advantage is very small, and the risk of erroding the tips and leading edge much greater on some runway surfaces. If I really need that last bit of advantage, I'd rather plan well in the backtrack, and begin to apply the power as roll around to line up, never coming to a stoip, particularly on soft runways. A fixed pitch propeller blade, and most variables are pretty well stalled over most of the blade with full power and no forward motion. You're just making lots of noise and drag, with minimal thrust, until you're rolling.