I accept that this might be deamed a slight digretion, but I do so anyway. Firstly I have to assume that 3 reds or 3 whites = .25 degree deviation from 3. Thus if you are JUST on 4 whites you are 0.5 degrees from 3 = 3.5 and JUST on 4 reds = 2.5 degress. There is an airfield I frequent where the PAPI's for the circling rwy are set at 2.5 degrees. Our circling procedure is designed to roll you out on finals at 3 degrees. The circling MDA could be as low as 400' agl. & the vis 2400m. The landing gate is 300' and for SOP's you have to be 3 reds or 3 whites at worst. You roll round on finals at MDA and min vis. You see 4 whites. You've got 100' to make the correction, but not at >1000fpm. It's all workable, but it gives the F/O as PM a fright unless you brief it. One solution is to extend the downwind by 5secs to create 3 whites at worst.
However, back to points raised above; you roll out stable on 3 degress, constant aiming point, constant speed, constant power all correct for 3 degrees, but 4 whites. At first it is confusing. Should PM call a G/A? That's their dillema.
Equally, 4 reds becomes a G/A which at some point must transit through 2 whites 2 reds i.e. correct Glide path; so why not make a sensible adjustment rather than a mandatory G/A. Surely Mk.1 eyeball can tell how low you really are, unless of course there is hight ground descending in the undershoot. The same true for 4 whites, Mk.1 eyeball. Could it be that most C.P's don't trust visual judgements anymore? And what would you do on minimum fuel at MDA at a non-radar airfield?
All I'm trying to say is perhaps the answer to the original question is not so red & white. As is much of aviation. We've just been brainwashed into thinking so.