So do an unencrypted normal site and an unencrypted attack site (like my spam folder is full of links to).
Most self-signed sites are fine, but because a few are MITM attacks, they should all throw big warnings (which users will learn to ignore, because of poor signal-to-noise).
Most unencrypted sites are fine, but because a few are attack sites, ....
The criteria for a user to enter sensitive info should not be "the connection is encrypted" or even "the connection is encrypted and goes to the server it says it does", but "I know the real-world identity of who I'm talking to".
The criteria to warn the user against entering sensitive info should be the negation of that; "I don't know the real-world identity of who I'm talking to".
The means of warning the user, should be such that the user does not need to act when not trying to enter sensitive info. So rather than pop-ups or interstitials that have to be dismissed -- and that the user can learn to dismiss -- there should be some persistent UI cue (like the green "Citigroup Inc (US)" beside the address bar) that the user can check when needed.
Browser: "Bad cert! The world's gonna end!"
User: "That's just a discussion forum, I don't care."
Browser: "Bad cert! The world's gonna end!"
User: "That's Joe's blog, I don't care."
Browser: "Bad cert! The world's gonna end!"
User: "yeah yeah, that's nice"
Browser: "Bad cert! The world's gonna end!"
User: "Would you shut up already!"
User: "...Why is my bank account empty!?"