How does this mean that TV is broken? Because you can't get instant access to every show ever created? That's not a TV problem, that's a you problem. That says nothing about TV. It does point to a weakness in distribution, but there are a variety of ways to get legally content these days: over the air, cable, satellite, online streaming (Hulu, Netflix), online purchase (Amazon, iTunes), buy or rent a DVD of a season of a show, etc... all of which can be played on a traditional TV.
If you want to make an argument, argue that distribution is broken. TV as a content production industry is still doing okay.
BTW - that was a good episode of the West Wing. While it was all done in flashbacks, you get to see the history of how people came to work in the West Wing. Donna's character particularly got more interesting after that episode. But you probably don't want to watch just that episode, it was the second half of a two-parter.
http://www.imdb.com/title/tt0745640/