I show pretty much the same way you're talking about. I never tried, but I think it is physically impossible to have a horse's mane braided for english and taking it down for western. Even worse if Western is first for you! English always goes first at my shows, but even then, it is impossible to take out the braids and make the mane look decent, because the mane will be kinky. Even if you do the running braid, you'll probably have to rush, and a rushed braid job looks bad. I don't suggest the running braid, because it pulls out so easily.
I always do button braids with my horse. I guess I don't have the patience to do the tiny plaits, because I'm a perfectionist when it comes to showing and would get frustrated if the braids weren't small and neat enough. For western, I just leave them in. Honestly, it looks fine. It shows off his neck, too! I guess some people in AQHA generally pick the discipline the horse is best at and do their mane based on that. If western pleasure was your strong point, you'd have the mane banded all day, or if HUS is your strong point, you keep it braided.
Riders aren't 16 and pregnant. Riders are 16 and arthritic.