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?
I actually think the main reason is that they are difficult to integrate with dynamic drivers.

Tonian does it extremely well, somehow.

They also don't have the dynamic snap of a cone tweeter.
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.