I seem to recall that this is exactly what a brand new installation of Thunderbird with Enigmail will do. I don't know if the newly generated public key is published anywhere, but that's a simple configuration change.
Yep, but Enigmail is not part of the default Thunderbird package. It has to specifically be installed by the user after installing and running Thunderbird.
I actually installed Thunderbird and Enigmail at the same time through my operating system's packet manager. You do not have to start Thunderbird before installing Enigmail.
Email encryption isn't mainstream and it isn't Thunderbird's fault, but GPG's. It's an antiquated protocol with an antique implemention and it's hard to understand and hard to setup. Thunderbird including the implementation by default would only confuse users. Those who want Enigmail already know to search for the plugin. Those who don't know what it is wouldn't know what to do with it.
