Something concrete would be....that perhaps you can see finer detail, a smaller font at x distance, or
a better resolution on the USAF chart. Something we can see, know, notice, and measure for results.
So....someone should be able to see some real difference before their eyes.
If a small error can cause a bigger problem than all the other aberrations combined
(Seidel is just summing the common types), and if
many or most binoculars are so misaligned, it should be easy to see the big aberration.
One concrete possibility is:
---looking at the same point through a line not on the center axis can cause abberration
Let's assume a fov of 8 degrees and a sweet spot of 6 degrees (over which you cannot see anything but the best sharpness)
---if the barrels are 30 arc-minutes out of line, the 'sweet spot' would be reduced from 360 arc minutes to 330 arc-minutes,
but inside that 330, you couldn't tell any difference from perfect focus.
That's all I can think would happen. Makes sense, given that I can read a 0.07" font from 36 ft, with one barrel or two.
It doesn't appear to exceed any other aberrations at all at that distance (and a 25 arc-minute axis difference).