Not that anyone would find this useful or practical, but I wonder if it would make sense to define an alternate protocol where the handshake is asynchronous and

Not that anyone would find this useful or practical, but I wonder if it would make sense to define an alternate protocol where the handshake is asynchronous and doesn't require the server to hold a continuously open connection while the client performs the encryption. This might be a non-starter for interactive applications, but for batch things like downloading emails (where you could get away with checking for new mails every hour or so) this could be tolerable.