It's funny how history and pop culture are so intertwined. The honor and formality in "pure martial arts" are constructs that served very practical reasons. We mythologize them when we don't really understand what they were(are) based upon...and especially when the come from the "mysterious East".
The structures of martial discipline are universal. Boxers understand them. Fencers understand them. Wrestlers understand them. Competitive martial artists understand them. I'll forebear going into them, because if you don't know, you'll only learn by doing number 1: Train, train, train.
So why are "pure martial artists" so obsessed with pageantry? Because it was, once upon a time, an effective barrier to "unwelcome-types" - i.e. commoners and peasants. Yep. "Pure martial artists" are elitist. In order to keep them in business, they have to propogate that myth. Ironic to a fencer, eh?
Karate wasn't bent on ceremony until Funakoshi introduced it to the Japanese cultural elite. Then "schools" formed. Schools designed to make money. Shaolin monks were about self-preservation. By proliferating an aura of mystique, they put another obstacle between themselves and their opponents. Once those problems went away, they were purely for, yep you guessed it, getting kids into martial art schools. Etc., etc.
I'm not ragging on the motivations of individual teachers, as they are for most part sincere. But the cause and effect exist.
I say this coming from a "pure" martial arts (classical Okinawan karate)background, having great success at the international level in competitive TKD and then becoming exclusively a fencer (with moderate success). At the highest levels, we're all doing the same thing...the only difference is the details: Technique, talent, and tactics.