Earlier quoted context omitted.
I don't know what you mean by 'leakable' exactly, but you can already mark cookies as HttpOnly (not accessible from Javascript) and Secure (only transmitted over HTTPS).
"Leakable" in the sense that you can hand it to somebody else and they can actually use it. A cookie is leakable because the client chooses to send it, so copying it to somebody else is really bad. A server-assigned per-connection ID is not leakable unless you can spoof the IP address of the one you're sending as.
Problem you may have is that some clients are behind proxy farms and can arrive with different source IP addresses within the scope of a single session.
If you do not bind the 'server-assigned-per-connection ID' to an IP address they become just as 'leakable' as a session cookie.