Could well be wrong, here, because I'm paraphrasing what I read in a publication a while back, but the demonstrated x-wind component is related to the side load the gear will handle without damage (plus a margin) and the aeroplane remain controllable, if the aircraft is landed without drift correction at that crosswind component. (Any volunteers to test that one?)
By a happy coincidence, that often seems to coincide with the maximum sideslip speed (side-ways speed) available at landing speed with full rudder.
I think it was a flight safety type journal; the article concerned how limits are determined for initial certification.
And, if remembered/interpreted correctly, explains at least in part, why so many of us can put one down relatively elegantly in more than the book crosswind. Especially if a higher than normal landing speed is used.
And right or wrong, wise or not-so, many aeroclubs I've been a member of had a lot of members, and often instructors, who were interested in relishing the difficult and trying out different ways of doing things. Not in a stupid, unplanned way, but in a thought-out, pre-planned way. (Well, sometimes not) And if it wasn't for attitudes similar to this, aviation just wouldn't progress much; improved procedures would evolve more slowly.
Re "jacking" the aircraft off the ground with flap, this is something I've tried, but would only consider using with manual flaps. Very direct reponse; no chance of flap runaway (had that once), and the reverse works well, too, that is, to abrubtly retract the flaps immediately after the flare, if there is any tendency to float coz you're a couple of knots too fast, or you get a gust.
Once again, I wouldn't do that with electric flaps, coz they go up slowly enough that lift produced, for the first few seconds of retraction, at the flare attitude, actually seems to increase briefly, then decrease slowly. Makes sense...if the wing is almost stalled flaring to land, then the area above the flaps is probably well and truly stalled, or at least closer to it. Raising them slowly might unstall the flaps, giving the aircraft an extra few seconds of float when it is least wanted. Plus of course, if at that point you need/decide to overshoot, you (or I) don't want the flaps retracting through 15 degrees on the way to nought. But with manual flaps, it can be real useful, and a tip I first heard about from an experienced bush pilot.
It seems though that this business of leaving the flaps up then lowering them at rotate probably wouldn't shorten the takeoff very much, because they simply ain't that draggy until a bit of speed has built up. I can't say for sure I've noticed any difference, it's just something I've played with a bit. The early 172's with the four-notch levers were real good in this regard, and gave the impression of using less distance,and with a more willing unstick.
I think PAFL has more to do with takeoff distance, than at what point during takeoff you lower the flaps.

Oh, by the way, in our little nanny-state, the hot water is limited to about 55 Celcius.