Tweeters are sealed units, they don't vent into the speaker cavity- so thye can't set up pressure waves.

The tweeter domes weigh milligrams- so they can't set up physical resonance.

They beam at all frequencies- so there's no air rpessure effects from the front of the speakers.

I struggle to see how a tweeter could ever effect an associated mid-range drivers break up. Only the crossover can do that if the mid-driver is run too open at the top end. So nothing to do with the tweeter itself and everything to do with bad crossover design and component selection- surely?