Well, yes, dispersion is another word for what we are talking about.

Group delay is the derivative of phase.

Dispersion causes non-flat group delay vs frequency which is the same
thing as non-linear phase vs frequency. (Note the term non-linear
here means NOT STRAIGHT LINE, it does NOT refer to non-linear in the
sense that the system is amplitude dependent. These are LTI systems we
are discusssing LTI= (linear Time invariant)

Yes you are correct, a device that has enough dispersion to create a
constant phase shift at all audio frequenices is very strange.

We're getting wrapped up in semantics. I'm done....

Mark