Thaumaturge is very academic, clinical? So it doesn't have a lot of connotations. Like, some men get very up in arms if you call them a witch. And wizard is, well, I'm not growing a beard. See what I'm saying? Harmless denotation, check! And why not? Nobody calls scientists "science users" so why can't we have a cool umbrella name!
I'm originally from California, but I've spent a lot of time in England and, recently, Scotland. Hordes of undead needed scorching. Big mess.