>>15sure it is, but then you're constantly generating private/public keypairs. this is slow, and so is using public key crypto for everything. PK crypto for everything is acceptable for e-mail because they're usually neither big enough nor frequent enough for this to be noticeable (although per-mail keypair generation would probably be a bit annoying), and you can't simply use Diffie Hellmann key exchange due to their asynchronous nature. in a normal HTTP connection, packets are sent often enough for this to considerably slow down browsing and there's nothing preventing you from performing DHKE.
tl;dr stop putting square crypto in round protocols, just use SSL/TLS (it's not perfect but it's the best thing we have now)