A writers' strike will wound traditional (broadcast and cable) television, but I don't think such a strike will kill it.
However, if a labor dispute cancels an entire NFL season (from preseason games through the Super Bowl), that could be something that broadcast and cable TV might not survive. The NFL, besides being the most popular fare on television, is also the greatest promotional platform on television to plug upcoming shows.
Without the promotional platform of the NFL, just about everything between September and early February on CBS, ESPN, Fox, and NBC (and to a lesser extent ABC, as they have a handful of NFL games) will see disastrous drops in viewership
Even networks that don't carry the NFL could be badly hurt: If someone tunes in a program on traditional TV that he/she sees promoted during a NFL game and doesn't like it, he/she could change the channel to a program on a network that doesn't carry the NFL, likes that show, and becomes a regular viewer of that other program.
Take away an entire NFL season, and traditional television could be practically dead.