I looked into using this, but changed my mind. Say you get a hit on Index.html. you probably want to push script.js and style.css.
So now you've pushed a few hundred kbits.
Now, the user comes back and asks for index.html again: do you send everything again? Surely the resources are still in the user's cache. If you don't, how do you know what to send? Only the user's browser knows what's in can't and what's not.
So you face the choice: speed up first visits but waste bandwidth for subsequent visits, out slow down first visits but speed up subsequent visits.