Again, parallel light focuses to a point, incident light does not, it has a series of points, the light is converging at the reflector. You just said incident light and then tried to explain the parabolic reflector in terms of parallel light.
Well then we can start with some basic definitions. "Incident" light is any light that impinges upon a specified surface. "Field of view" is the extent of the viewable area of the telescope. "Coherent" means that all rays are in phase, that is, the sum of all rays produces a pure sinusoid.
As I understood your complaint, you're saying that any two rays that are phase shifted on account of the parabolic mirror combine to simulate red shift (or blue shift). My statement to you is that this is incorrect, because the star light is not coherent to begin with, and additional phase scattering by the dish will have no meaningful effect on the phase information, since it was random to begin with. Furthermore, phase shift is not equivalent to red or blue shift. Frequency shift (over the spectrum) is. Therefore, you can't simulate red or blue shift simply by introducing a parabolic mirror.
I'm not talking about longer path although that will occur to some degree.
Optically you will only see the aberration at the limit of the optics, even though you will loose some resolution, it's when you refract the light after it passes through a series of focal points, the light will NOT be parallel, it will be divergent before it gets refracted, you've gone and designed the instrumentation based on an ideal model that only works for spherical chickens in a vacuum....
This still makes no sense. All light rays within the field of view of the mirror are pseudo-randomly phase shifted upon arrival at the focus. But each and every ray retains its original frequency content. Since the phase information is random to begin with, this additional phase distortion is not going to alter the spectral content. That is, you need frequency shift, not phase shift, to simulate red or blue shift. And that's the part that is preserved in a parabolic mirror.
The world isn't wrong at all,
If through experimental observation it is found that the redshift better fits a model based on an aberration, the data collected isn't wrong, I doubt there would be much sleep lost, in fact the improvements to optics and astronomy would outweigh any losses.
It's completely testable, or are you going to not test it because light is parallel?
By you analysis, every parabolic dish in the world is inherently defective. That's a huge indictment against a large population of very smart people. It makes no sense. You seem to be assuming that nobody tests or calibrates their precision instruments which is ludicrous. Also note, if this actually occurred as you think, it would be advantageous, because passive devices could be built out of dishes which produce ultrawide band spectral shifting (such as a downconverter). It would improve signal to noise ratios in some cases and open new doors to technology.
Unless we're still speaking a different language, you would have to demonstrate a frequency shift, not a phase shift, that arises out of using a parabolic mirror. But you can't, because it doesn't, hence my remarks.