The other thing is that renegotiation is somewhat broken since that related security flaw in 2010ish, so you can't have parts of a site accessible without client certs and other parts requiring a cert.
This has been fixed since, but I don't know how well it's supported by clients.
Finally, compared to 2008, we're using many more devices for accessing various web applications now. Having the client cert bound to one browser on one machine is annoying and synchronizing it truly securely is probably impossible.
I do stand by the horrendous UI though. Even if the other issues weren't there, the UI certainly kills client certificates for normal users.
Then again, crypto UI is hard and I'm afraid the incentive for redesigning this is pretty much zero because nobody is using it to begin with and because it's flawed anyways.