ORIGINAL: BMatthews Cola, I think you may not have some of your Cp locations quite right. It's been a while but I seem to remember that the Center of Pressure tended to move forward with increasing angle of attack until at the stall it was at the leading edge or perhaps it was said to "fall off the front" of the leading edge at the stall point or such thing.
Yes, I sort of remembered that too, but I wasn't sure.
However, it seems the reflex-cambered (with upwash) wings have CP in infinity, but forward of the wing, so as the AoA increases, the CP acually moves backwards until it reaches AC and then back forward to infinity. I'd guess that in reality, for zero lift, the CP is situated just in front of the leading edge.
As for the "falling of the front", it seemed logical to me too, but when you think better, you'll see that it's impossible (I think, at least), because when the wing stalls, it actually doesn't get zero lift immediately (and how would you get lift from a wing whose CP is outside its lifting area?), but depending on the wing type, looses Cl gradually and during that time CP moves back to original zero lift position, but this time with AoA 90° or so.
Why is a stall point behind AC? I think because, AC is a point where Lift/Drag coefficients meet and thus wing has the best effectivness. Stall point is beyond, because wing has some more chord to produce more lift, but beyond AC point drag rises exponentially to AoA.
But now, the more I think of what you said, the more I believe it was something like that. I mean I think I remember something like CP falling from the leading edge, but maybe those were upwashed (stable) wings or something.
As for fixed CP, I'd agree it's easier for calculations and I'd probably use it myself if I was to calculate an aircraft. However, I find this "traveling" CP explanation way better explainatory in terms of chordwise dependance. It's less abstract and proves direct relationship between chord and max.AoA.
Any finally, why does CP moves at all?
I think it's because of lift/drag resultant and the cambering. Cambered wing is unstable, with pronounced pitching moments (either up or down). So, as the AoA raises, the CP moves forward because lift vector is getting larger and larger and more parallel with chord. After AC, the drag component becomes dominant and results in CP's moving backwards.