If P2P were a "first-class citizen", the initial handshake wouldn't take longer--it would be faster!
Suppose that my city's newspaper (or TV station) monitored the (socially accepted, widely adopted) P2P networks for reliable mirrors of their own content, then sent each user's browser hrefs to the mirrors, rather than their own site.
The more popular the content, the more likely that your next door neighbor's P2P system can stream it to you.
Since running such software is socially acceptable in this hypothetical future, your P2P software doesn't have to go through the 'discovery' step. One of your hostnames is 1234.main.st.ci.lincoln.ne.us (see http://owen.sj.ca.us/~rk/howto/usdomainname.html) and one of them is mirror5.journalstar.org.ci.lincoln.ne.us. Everybody on Main St already knows your IP address, and if you mirror a lot of content, they might even have an existing active connection... you see where this is going? :)
Suppose that my city's newspaper (or TV station) monitored the (socially accepted, widely adopted) P2P networks for reliable mirrors of their own content, then sent each user's browser hrefs to the mirrors, rather than their own site.
The more popular the content, the more likely that your next door neighbor's P2P system can stream it to you.
Since running such software is socially acceptable in this hypothetical future, your P2P software doesn't have to go through the 'discovery' step. One of your hostnames is 1234.main.st.ci.lincoln.ne.us (see http://owen.sj.ca.us/~rk/howto/usdomainname.html) and one of them is mirror5.journalstar.org.ci.lincoln.ne.us. Everybody on Main St already knows your IP address, and if you mirror a lot of content, they might even have an existing active connection... you see where this is going? :)