Increasing the resonant frequency by increasing stiffness has merit in a three (or more) way 'speaker with separate enclosures, such that the bass cabinet resonances are moved up into the midrange, where even though the ear is more sensitive, the bass cabinet won't excite those frequencies as they're outside the bass passband. It relies of course on steep crossover slopes and well behaved drivers. Ditto for the mid and HF, where resonances can be pushed up out of the way. In a loudspeaker with a single cabinet, the Harbeth approach makes a lot of sense.
Tweeters, especially metal-dome tweeters often have 'oil-can' modes which need to be kept away from the audio passband. One undesirable consequence of so-called HD audio and high sampling rates is that loudspeakers now need, for marketing reasons, to go way above the audio band where it's pretty difficult to avoid tweeter resonances.
S.