You won't get a faster web, you'll just get more cruft shoved on each page.
Example: Buzzfeed loads in 1 second for me on my work's broadband, but it's still full of junk making it hard to use. Bandwidth-wise, it could handle more crap on the page, but in terms of usability it's at the limit.
I think you actually will get a faster and generally improved web when sites are finally able to end HTTP/1 support, because it will free up web developers from old performance hacks like asset concatenation, image sprites etc, which add a lot of friction to making websites.
All that said, this demo is bullshit for the reasons given in other comments.