I think maybe many of those many tabs you have open may be facing sites that don't need to keep the connection to you open after the data is transmitted and so will just get closed... in the mean time, if one of those pages has a long URL you've used to access it (which includes form GETs), that URL gets sent to each subcomponent request of the page that needs fetching (images, iframes, scripts) as the HTTP REFERER... as does any set cookie string. While a protocol that allows you to send those only once may not be a big win for you, for a server that's dealing with tens/hundreds of thousands of requests a minute, that's a massive saving, as it is for the series of tubes connecting that server to you.
For sites that do want to keep the connection open there could be additional savings for the server. Imagine the normal process of doing this (for instant message delivery etc) involves you opening a connection to the remote web server, which parses your request, and then fires up an instance of perl or php etc to handle it. To hold the connection open, that instance of perl/php will stay running, holding the connection open, and printing to it should it need. With a multiplexing connection this needn't be true; a minimal connection handling server can stay running, holding details of the connection (inter-connection persistent headers etc) in its memory, but allowing the script process to unload until next needed again, if it's needed again. The other option is that other request handlers may be able to open a channel to you through the held open connection and send data to you. Without this (assuming an instant-messenging model) both the sender and receiver of the message would each have their own instances of the script processor running, with the process handling the senders request connecting to the process handling the receivers request, and sending it the message which it would then bounce on to you.
So yeah don't worry about it, this should all mean you can keep all your tabs open, and now with up to 50% less guilt! :-)