This has been tried by a dozen or more different altcoins over the last decade (including one on BitTorrent itself!) and always fails with the coin's price collapse. Weak sauce. You'd think someone would make a proper bitcoin-only client but I've yet to see one done correctly.
However, there is one issue that the bittorrent community constantly brings up that you shouldn't overlook; Monetizing every file download will make the community ethos change from people who feel they are helping the world by sharing information freely to... A marketplace. Many of them swear that the day such a monetized torrent client is popularized is the day they subscribe to netflix.
I personally believe these folks to all be commies, but damn, there are a lot of commies on the internet.