One of the problems with collecting files (say, video) via bittorrent is that it requires that other people be interested in the same file you want at the same time that you want it. If you missed last week's episode, and just got back to civilization, everybody's gonna be sharing this week's episode, and you'll be lucky to get 29 bits per second from someone who has 1/5 of the file.
Yes, bittorrent's technology for binary file distribution is way better than NNTP, but Usenet News has, as has been amply explained, a lot of reasons it's still good technology.
Yes, you should complain to Time Warner that they took away a service you used and didn't charge you any less.
Yes, it would probably be smart to find another server, and preferably make a donation to help keep them running.
Everest, btw, still has news servers, and I believe it costs less for the same bandwidth.