CBS All-Access is a good example of a single channel app that offers live television. However, CBS All Access doesn't contain CBS's complete library so don't go in expecting you'll be able to stream the entire Big Bang Theory series. Other networks, like HGTV, Smithsonian Channel, History Channel, etc. also offer varying degrees of access to content through their apps.
What you get: YouTube TV offers access to live TV from up to 50 providers, including all the major networks. It also has a cloud DVR with unlimited storage. The service is now available in more markets after launching in five cities in 2017. You also get the original programming on YouTube Red Originals. You can add Showtime for $11 per month, CuriosityStream for $3 more per month, or AMC Premiere for an additional $5 per month.
The question of "when does it make sense?" can easily be rephrased as "how much money can I save?" and one of the biggest factors will be the price difference between combined internet and TV service or just internet. These are also the options that vary the most widely based on where you live, and the availability of promotions or contracts that can keep prices down for a short time.