Comment by kaoD

Although such scheme is indeed safer than HTTP (protects against passive attacks), what you're describing is not self-signed certificates, but merely encryption (with new random _unathenticated_ keys per session).

Keys would be exchanged via Diffie-Hellman as usual, but a certificate wouldn't be involved since it's useless anyways (you can't certify anything in such a scheme, why bother at all?) and thus would be vulnerable to active attacks.

Certificates imply long-term authentication. It's an important nuance since they are long-lived by definition, so they have to be trusted and revoked as needed, in which case we're still facing the problem I mentioned earlier.