In 1987 my physics professor presented this proof to our class -- I always wondered why this elegant derivation of the Lorentz transform was not more widely used in undergrad physics education.
As a first introduction, its more instructive to develop physical theories from physical postulates (like speed of light is constant), rather than constraining possible theories using more abstract mathematical principles.
Undergrads will not appreciate the latter, as much as they will the first. Especially, because in the third semester, where relativity is first introduced, most physics undergrads don't know any group theory.
The contradiction between Maxwell’s electrodynamics and Newtonian mechanics was the raison d'etre of the relativity foundations laid out by Lorentz, Poincaré and Einstein. And since those subjects are usually studied before the theory of relativity, I think it makes sense to piggyback on them and use the historical reasoning to build the intuition behind relativity.
Undergrads will not appreciate the latter, as much as they will the first. Especially, because in the third semester, where relativity is first introduced, most physics undergrads don't know any group theory.