At the stall we have a high AoA - this creates a risk of secondary loss of control, and also high drag - which bleeds energy off and causes a high rate of descent.
We wish to do two things initially - ensure that there is no secondary loss of control (most important) and reduce height loss (a bit less important).
So we move the stick forward and simultaneously (UK, EASAland, Australia) or just after (FAAland) apply full power. The stick reduces AoA, the power reduces height loss by putting more energy into the aeroplane.
Whilst the aeroplane is at high AoA, we want to avoid two things - (1) sideslip, (2) any further pitch up.
(2) Is ensured by not applying power before the pitch input, as in most aeroplanes there is a nose-up pitching moment with increased thrust. Yes, I know we hadn't mentioned that before, I'm just including it for completeness and before anybody starts talking about the equally henous practice of powering out of the stall.
(1) - sideslip, is avoided by using the rudder to keep the aeroplane in balance. Depending upon what you've got in the particular aeroplane - a yaw string (gliders mostly), beta gauge (a few hi-tech aeroplanes), slip ball (most aeroplanes) or sense through the seat of pants (anything) will all tell you whether the aeroplane is in balance. In very simple, but correct terms, an in-balance aeroplane has no sideslip.
However rapid the stall entry is, however much wing drop you have, whatever other motion is going on - if there's no sideslip, there should be no secondary loss of control (most likely an incipient spin).
The reason for not using aileron is exactly the same - any use of aileron will cause some sideslip. The design of the aeroplane will change the maginitude and sign of that, but is near certain not to eliminate it. So we keep the ailerons neutral.
If you do anything whatsoever with the rudder apart from keeping the aeroplane in balance, then there will probably be non-zero sideslip. If you do anything with the ailerons apart from keep them neutral, there'll be sideslip. With non-zero sideslip, there is a risk of 2LOC, and thus risk of a spin.
It doesn't matter whether you try to pick up a wing, prevent further wing drop, prevent further yaw - call it what you like; ANY use of rudder apart from to keep the aircraft in balance, is likely to result in non-zero sideslip, and thus a non-zero risk of a spin.
(Which is pretty much what BEagle said, just I used more words).
G