You're correct, but there are implications to your point.
Granted that Uryuu knows combat sword techniques and is considered an expert, and Bart not using his magic has worse technique than Uryuu. If "Martial Arts developed without magic are superior", then Bart should get whupped by the expert fighters of every region. Because every fighting style on Earth is built without Magic. This is a testable premise, Bart just has to fight and lose to a dozen champions of multiple disciplines.
I won't take it back until Bart gets punked by Karate, Kung Fu, Muy Thai, Boxing, Sabat, Sampo, Krav Maga, Capoeira, Bayonet Combat, etc. I demand the crossover with Kengan Asura.