You don't want to make https://mybank.com allow self-signed certs without warning, because the "s" on the end means both "try to encrypt" and "I expect this url to be MITM-free". What was a secure bookmark to a MITM-protected url would no longer be MITM-protected at all. That's a decrease in security.
This is what RFC 2817 (not implemented by anyone) would be useful for.
The right thing to do is to leave https:// alone, but to add the ability to encrypt http:// transactions, without requiring that MITM-protection be present. If http:// urls could be automatically encrypted whenever both the client and server support it, that's a pure win. Even more so if all the popular servers were configured to have that work out of the box.