Reading all this, I'm beginning to understand why most morris music sounds so dreadful. I guess the decent musicians are driven away by the cloth-eared melodeonists etc.
My particular bugbear is the use of the bass drum - it often seems to be handed to somebody who can't play anything else, usually for the very good reason that they're completely unmusical. The usual style seems to be to whack it as hard as possible, so you get a completely toneless thud which totally drowns out the rest of the music. If it's in time with the dance, it's a bonus.