up/downwash do already happen in the 2D "airfoil" airstream (at least when flying subsonic). Additional downwash happens due to the finite wing in the 3D "wing" airstream.
According to the 2D airfoil theory of the conformal mapping (mathematically "projecting" the airfoil on a cylinder) you only need to calculate the speed- (and according pressure-) distribution for 2 angles of attack, and can interpolate linearly in between. This is why measuring pressure on two locations along the airfoil is an efficient way of measuring the local AoA at that spanwise position. As long as you have no friction and hence no flow detachment and no boundary layer, of course.
With all the complex 3D effects (e.g. due to the fuselage, propeller slipstream, flap/aileron deflection, maneuvres etc.) this information is not "the" AoA of the aircraft, it may however do exactly the job which is required: giving an indication of the margin to stall.
I am quite sure that the theory of conformal mapping allows an exact assessment of the up/downwash for airfoils with a constant radius arc skeleton line (used on many popular airfoils up to WWII), so some up/downwash and zero lift information relative to camber can be determined easily and accurately. I am not too sure that this information is very useful except for a hand full of academics. Pilots will never ask for such information.
I assume that up/downwash is much more depending on Cl than on camber (although at a constant AoA this basically means the same), and Cl is much closer linked to the overall aircraft situation, and hence much more important for pilots.
The problem is, that the higher the Cl, the higher the upwash at the leading edge hence the higher the AoA you measure there. If the wing starts to stall (and it is a good airfoil where flow gradually setaches starting from the trailing edge extending forward), this will reduce Cl (or reduce the slope of the Cl curve), which will also reduce your AoA measured. So just when you get close to the warning threshold, when AoA gets critically high, your measured AoA indicates a lower (and hence less critical) value, so it does not accurately warn you.
With a bit of margin, such systems still work well. They will warn you a little early, but there is no point in operating very close to stall anyway, except you are thermalling in a glider...