why aren't ribbon tweeters more popular?

What is the downside to ribbon tweeters? I haven't had any in a long time (Phase Linear P580's, stolen, still miss them.) Ribbons offer great extension and speed; other than expense, what objectionable qualities limit their use?
The amk2 Is one of the better hi frequency transducers available but RAAL ribbons are wonderful in there own right and 1 can design fine sounding loudspeaker with either transducer. Where design would be best if a amk2 is used a ribbon wouldn't be the best choice, same where a RAAL would work best that design wouldn't be so good for amk2. Hope this makes some sense ;) They are not inter changeable.
I think the down sides are dispersion patterns (in some designs) and difficulty integrating them. However when implemented well they I find them excellent.
Agree with Ojgalli statement of "Downsides — delicate, easily overdriven, higher distortion, beaming dispersion pattern."

These are well known and accepted drawbacks to ribbons and it answers the OP's question of why they aren't used as widely as other types of tweeter.
Shadorne modern ribbons are not easily over driven. And they do not have distortions thats are musically significant. Much of the - about ribbons of late comes from Zaph audios test link. To some cheap ribbon dome comparison. But if they looked more they would see Zaph is offering most loudspeakers with ribbons. And RAAL has eliminated the dispersion issue which isn't hard at all for a loudspeaker designer to work with. And can be an advantage. I have never had a ribbon loudspeaker KCS manufactured returned due to ribbon damage. And if it did would be a easy repair. I see so many loudspeakers using ribbons today I thought about listing but just to darn many so the whole premise that ribbons are not popular is just not true. Sure more domes about but then they are far more affordable and thats why so popular.