Edit: found the comment from Adam Langley [0]. They didn't want to add it to Chrome because it wouldn't meet standards for the preferences UI inclusion, practically everyone would just rely on the default notaries, so Google would have to guarantee notary uptime, thus being forced to run them on their own.

He doesn't really point out why they don't include it as an optional alternative without any notaries pre-configured. He does however say that running it as an extension would be fine, but the required APIs weren't available at the time of writing.

0: https://www.imperialviolet.org/2011/09/07/convergence.html

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/

Your web browser grinds to a halt because almost no one runs a notary. I tried using it for a while.