I think one of the reasons the torrent protocol is not built-in is that it's simply more complicated and the user experience is not as good.
Or perhaps it is because there is a certain stigma attached to using a technology that enables distribution of data, even when it is against the wishes of the creator of the data.
That's self-fulfilling - if it were built into the browser, there's no reason you'd really have to know.
(Presumably you wouldn't run into the "zero-seeders" problem if the servers acted as seeders - they're currently serving 100% of the file anyway (without torrenting), so torrenting would only reduce that.)
I don't think the complexity and user experience issues are completely intrinsic to the protocol - BitTornado (sadly, another client that misbehaves, and hasn't been updated in 6 years) was hands-down the easiest for less techy people to use and understand. (Each download has its own window and instance of the program, making it look and feel very similar to downloading in Internet Explorer)
Why do you say the difficulty is in hashing the entire file? BitTorrent divides the files into small chunks and hashes those, so downloading lots of small files vs downloading one big one doesn't make a lot of difference
(with a few caveats - some clients support an additional hash on each file, which can save you re-downloading data if two files share a block and only one is changed, and some clients add padding data so there is only one file per block. In practice, these are both very rare)
It's a problem we have in my house with Spotify, which utilises P2P to lower costs - it has a negative effect on anyone else who is gaming.