It's a tricky business running a torrent site. Unless it is fully decentralized, it can be shut down fairly easily.
Starting a torrent site using the HTTP & DNS protocols is a lost cause. HTTP can be worked around, but DNS is very problematic. I think we'll see more and more torrent sites show up that leverages IPFS[1] or ZeroNet[2], but the second the main browser vendors adds support for something like IPNS (decentralized alternative to DNS), torrent sites will have won the battle with MPAA, RIAA and other IP and DMCA enforcers. Considering the grip that the movie studios has around the vendors, it is very unlikely that it will happen.
Don't forget Freeenet https://www.freenetproject.org/, which has the goal of anonymity. IPFS isn't anonymous and the IP address of users pinning the content is easily discoverable.
Freenet has at least one site that lists magnet hashes and inserts some of the torrent content directly into the network.
I believe the main problem is how the site owner can remain anonymous and still collect the advertising revenue. The hosting does not seem to be so big issue, since these well known sites have been running for quite a while.
Yes it is decentralized, but it relies on central authorities to work, which in turn relies on a stable, cross-border legal system - which many believes is currently not in a good state (see Freak_NL's response for example: https://news.ycombinator.com/item?id=12230903 ).
People have different views on this of course, but I think we all can agree that it needs a major overhaul to make the majority happy (the legal system that is).
Since Mozilla didn't shy away to include Adobe Binaries in Firefox to decrypt Movie-Streams, i'm pretty sure for IPNS we're going to get a unmodifiable Blacklist so "Bad"-Sheep can be blocked.
Starting a torrent site using the HTTP & DNS protocols is a lost cause. HTTP can be worked around, but DNS is very problematic. I think we'll see more and more torrent sites show up that leverages IPFS[1] or ZeroNet[2], but the second the main browser vendors adds support for something like IPNS (decentralized alternative to DNS), torrent sites will have won the battle with MPAA, RIAA and other IP and DMCA enforcers. Considering the grip that the movie studios has around the vendors, it is very unlikely that it will happen.
[1] - https://ipfs.io/
[2] - https://zeronet.io/