It's also a good way to distribute free content, or large content, or to get a copy of paid content which isn't crippled by DRM.

This system could be made to work, but you need a significant number of bittorrent peers/tor nodes accepting payments before it would make any noticeable difference. As with bitcoin itself, adoption is probably the main hurdle.

Also, paying peers (in bittorrent) to preferentially send you content wouldn't actually speed up the network, it would slow it down overall. For one, you often only receive a block of content when you've uploaded some yourself, so this ensures that most peers at least upload something if you circumvent that some peers will spend their bitcoins to leech off the network. Secondly, and more spychologically instead of technologically, if people are paying for their bittorrent downloads they're probably going to leech; "I've paid for this", they think, "So I don't need to donate bandwidth and get a good seeding ration too".