The next time you are in the studio try this. Take one of your favorite rock mixes. Pick something with a conventional bass track, no slapping or popping. Listen through it two or three times. Now filter out everything above 5000 hz on the bass track. A 24db cut will work. Listen again to the full mix. Can you tell the difference? Over the years I have done this with a blind A/B comparison for a dozen studio engineers. Only one of them could tell the difference. Does it mean that everything in a bass track over 5000 hz is irrevelent. Probably not. But it sure demonstrates where your 10,000 hz tweeter fits into the big picture. As for the "mud" in a live performance, in many cases it's not the bass. It's caused by the microphone on the kick drum. Especially if the drummer has a busy foot and the soundman likes to watch the cones flapping back and forth on the subwoofers.
Most tweeters seem to be crossed over around 3K or so, and most drivers fall off below that. It's not just about 5K+ sizzle, although that can be a beautiful sound in some contexts.
A well designed crossover and tweeter, like in the new TecAmp cabs or Epifani cabs, can provide a nice, natural, subtle extension up above 2K or so that really sounds beautiful and natural (again, for some basses, using bright roundwounds, for certain playing styles).
Cabs with those little mid drivers are a nice 'in-between' solution for those that don't need the full extension of a classic horn type tweeter but want a little more upper mid definition than the upper range of most drivers can supply.
That being said, I agree that there is NOTHING worse than a cheap crossover and harsh sounding tweeter in a cheap box. But, that's just poor execution.
I again never could figure out why those of us who use and love two and three way cabs can understand those that don't, and it doesn't happen the other way around. Strange to me

The only think I can think of is that the players who are attracted to a more vintage sound, in general, aren't really aware of players like Anthony Jackson, Richard Bona, Lincoln Goines, John Patitucci, Nathan East, Jimmy Johnson, Victor Wooten, etc., etc., etc., all of whom use some sort of two or three way cab with tweeter as backline.
I guess following up on that point, if your only experience with two way cabs is an SWR Workingman's 410, or something like that, I would hate tweeters also
