I like it too. The cons just don't exist in my pow:

one downside was that it didn't work on things like airport access points, but those break regular tls too.

an other downside was the fact that google didn't want to integrate it in chrome because the notaries would have to be always up. now they run transparency logs that have to be always up anyway. so.. what's the difference?

The Perspectives Project piked up the idea, and it seems less dead that Convergence: https://perspectives-project.org/