What is the source for the "rule" forbidding configuration changes below 200ft AGL?
There is no rule.  There is a convention that you should be in a stabilized condition that requires no major control inputs or power changes in the last few hundred feet.  With jets, airlines often have an operational policy that requires a stabilized approach configuration once below 1000 ft to continue with a landing.

The reason is pretty simple.  If I'm well outside a descent rate or speed parameter close to the ground, I'm forced to attempt a much more radical correction, because I don't have much time, than I would farther out.  The radical correction will, unless the pilot is very experienced and proficient on type, invariably result in an over correction, and the result is oscillation about the target parameter just as the moment of truth is approaching, and from there things get entertaining.

So in training it's a mantra that is almost universally taught that you need to be settled in on slope and on speed when getting close to the runway.  On little airplanes, a couple hundred feet, on bigger ones, maybe 500, on transports, a thousand.  The more the mass and inertial involved, the farther out you need to be settled in.

If you are sufficiently skilled and experienced on an airplane type, all this is not quite that critical, but for a newer pilot it's pretty important.

The stuff about using the last bit of flap to stretch a glide doesn't work.  It might theoretically help you make it across a ditch before touching down if you were cutting it that close with an engine failure, but more likely it just steepens the glide angle and makes things worse.