I can't think of a network related app I ever used where hostname based auth wouldn't be a net plus. Mail, chat, web browsing, VPN, VNC, network filesystems, ... Not to say "as long as I know that it's the right host, all my encryption needs are satisfied!" Sure, sometimes you want more. But knowing I got the host matching the hostname would always help.
As to the UI: Yes, but that's precisely because it is currently unclear who is responsible. Java has its own keystore, FF has its own but Chrome doesn't, even some libraries have their own or they don't, depending on the OS. It's a mess. A mess that I don't care about, as a user.
I want a central key store that apps tap in to. When I revoke a cert for Diginotar, I don't want to have to grep every file in my entire filesystem for that string on the off chance some crazy statically linked lib installed a local cert store somewhere.
And sure, an app wants to create a special case just for itself (e.g. a client certificate only for mail), let it. But I'd like that to be the exception, not the rule.
Cert management is a mess right now, and both developers and users are duped.