Hello cough
Which AA are you talking about? Lots of companies impose one (Ryanair for instance impose an MFRA of 1000 feet) and at Ryanair if you raise the flap before you have gone through that you'll get into trouble. But that's not a directive from Boeing. I have found a reference in the Boeing 737 classic training notes that suggests the minimum height for flap retraction is 400 feet but its the only manufacturers recommendations I can find.
If there are company imposed limits that's absolutely fine and you can't breech them but it's still okay to understand why they are there.
We call it AA, min height for change from takeoff thrust to climb thrust. Doesn't matter what the term is, its the meaning...
Another 400' reference that I have found is contained in the 737 QRH. It contains the normal takeoff profile which shows earliest points for things to happen. 400' is the earliest point you start anything...
Takeoff profiles - From what I've read, you maintain max thrust till after flap retraction, we reduce thrust before. To accelerate to 250 kt (initial climb speed) takes a few miles (at 1000fpm ish). So say I were to start that after take off once the gear is up, we would be flying very low for a few miles and trust me, if the company didn't get me the journalists would (for low flying...)(rightly...)
Lastly, You've said that clean at V2+20 you get a better climb rate than with flaps out at V2 and you have the graph to prove it. I accept that, but a quick question is, do you have a climb graph for takeoff flap and V2+20? Improved climb is a well researched area...