"Quod erat demonstrandum" means "which is what had to be proved". There's another Q.E.D. meaning "quod esset demonstrandum" and means "what would have to be proved". I always read a lot of you equivalencing folks - I just don't see real pictures In theory perspective remains the same when subject and object keep their distance and angles. I agree with that.
In practice, there are limits at least optically: Just switch to 20 m and say the same about about a bench in a park, taken with a wide-angle and the other with a tele - perspective and compression remain the same, I know, but is only one property of the picture - the others are resolution and contrast i.e.
What you're saying about equivalence is only valid if you'd be able to shrink all (not only a couple) properties of a camera and lens combination. If it would be that easy, we had as a consequence not to deal with different kinds of bokeh. All the other differences would be equivalented? I doubt that. The various constructions of wide angles which cannot be made easier due to the flange distance have an impact on IQ as well. It is not "all the same, just smaller or larger"