It should be possible in theory with modern JS frameworks and HTML5 features. But there would be a lot of additional implementation, which usually is delivered by existing libraries (whole cryptographic stuff for example). Other problems I can think about right now is efficiency (interpreted language) and JS language itself - it was not designed for this kind of purposes.
And final question: what do you need it for when you have normal applications?
Well, I was thinking in terms of ease of use for users (everyone has a browser) and developers (a lot of js devs out there) to help ease adoption. I know that we know have bittorrent clients developed on top of WebRTC (http://webtorrent.io), so I was wondering if there's something that makes this impossible or a bad idea?
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Other problems I can think about right now is efficiency (interpreted language) and JS language itself - it was not designed for this kind of purposes.
And final question: what do you need it for when you have normal applications?