That said, I don't think piracy is to blame here, but more the murky nature of copyright in general, with BitTorrent you automatically become redistributor of everything you download and that's just a huge liability and privacy risk that I can easily see browser developers wanting to avoid.
Also browser developers have gotten lazy, they couldn't even find the resources to keep FTP alive, so I doubt BitTorrent would have survived for long even if they tried adding it.