This is a bit of an unjust to the history of sociology, and science writ large. What Weber does is help establish, axiomatically not experimentally, the base definitions for the system of sociology. So yes, it is a fiction from another system, but it must be assumed true in that system. This is, ironically given your accusations, a purely mathematical approach to creating a field.

It is taught in 101 because it is important when teaching a subject for the learner to be able to answer “And what again are we doing here?”

The physical sciences have no less "old white man conjecture" in their history.

They have but is not taught as science. Physics 101 does not study Aristotles ideas as part of physics. Not because they are wrong but because they are not scientific. They start with Galileo and Newton.

The first chemistry lecture I ever had started with something to the effect of "Chemistry emerged from alchemy, and we'll not speak of this again!"