Continuing in your rant: technically, you still expect the server to behave correctly and ask your browser for the encrypted text through a special <textarea>. If the server doesn't want to send the it, it won't.
What I see is going the other way around: have the browser detect a standard <textarea> and provide control to automatically encrypt what you typed. Something ala https://www.mailvelope.com/. No changes in the websites. You can do it today (well, if you have the good plugin/browser).
Now I think the real hard problem is not encryption itself but key distribution. You need to find a way to reliably tell other people "This is my key", but you need some interactive way so that I don't need to wait for you manually sending me your key in order for me to send you something encrypted... I believe XMPP is much better suited for that (there are ways to exchange content between people, even when they are not connected, for instance through services), so maybe Gmail could build something on top of SMTP+XMPP to exchange keys. And that still wouldn't be truly authenticated, only optimistically, because in the end trust is something only users can set.
Sure. The site shouldn't be able to imitate your textarea. First, it should have no access to your keyring and whatever, so it won't be able to crudely imitate the UI. Then, browser should have some sort of indication outside of site's control, that shows whenever you're editing text in a secure area or not.
As for key distribution - if it would work opportunistically, it would be still a great achievement. Like, all emails I send are signed, and recipient MUA can figure out my key ID from those and retrieve it automatically. Then proceed to suggesting encrypting the correspondence. If so, the UI should clearly indicate that communications are encrypted but noticeably warn that identity's not verified. That is, solving one problem at a time, I guess.
What I see is going the other way around: have the browser detect a standard <textarea> and provide control to automatically encrypt what you typed. Something ala https://www.mailvelope.com/. No changes in the websites. You can do it today (well, if you have the good plugin/browser).
Now I think the real hard problem is not encryption itself but key distribution. You need to find a way to reliably tell other people "This is my key", but you need some interactive way so that I don't need to wait for you manually sending me your key in order for me to send you something encrypted... I believe XMPP is much better suited for that (there are ways to exchange content between people, even when they are not connected, for instance through services), so maybe Gmail could build something on top of SMTP+XMPP to exchange keys. And that still wouldn't be truly authenticated, only optimistically, because in the end trust is something only users can set.