Circuit-switch routing can be beneficial against situations like the one described on the previous slide. With this kind of routing, we can't have contention for a link because the entire communication channel is reserved before the communication begins. All the costs associated with sending a message this way are therefore paid up front -- they only occur when you allocate the communication channel.
However, circuit-switch routing isn't the best use of a network. Once we reserve a communication channel, we hold onto that channel until the communication is complete, which is why more fine-grained, packet-based switching systems are usually far more efficient.
The analogy discussed in lecture was about traffic.
If a car wishes to drive from Pittsburgh to San Francisco, a circuit-switched routing would reserve the entire path first, before letting the car start. Apparently, there is an enormous cost associated with this approach, and eventually only one car is able to use the road (horrible utilization). On the other hand, we are guaranteed to have no traffic along the entire way.
An alternative approach is, of course, to use packet-switched routing for better granularity.
Circuit switched routing is also helpful when latency is more of an issue than network utilization. The lack of contention means that latency is the same once the links have been reserved, while with packet-switched routing latencies would depend on other traffic in the network.
But you still have the latency of waiting for the appropriate links to free up before you can reserve them. It is not obvious that this results in lower latency than using packet-switched routing. It probably depends on other factors like packet distribution.
You're correct that it doesn't guarantee lower latency overall, including setup and teardown. I was referring to the latency of transmission itself as being lower because you have a reserved link.
For larger networks, the telephone line vs. Internet example works well to demonstrate this. When you're having a conversation, you need the audio data to arrive in order with as little delay as possible to be able to make sense of it at all. Otherwise you'll just hear garbled noise. With most Internet packets, it's fine if some packets arrive earlier or later, as they can be reassembled before being used without any consequences.
This example does bring up the question of how Skype/Google hangouts/calls over the Internet work. It seems that voice-over-IP (what's offered by Skype) tries to mimic the direct linking of circuit-switched routing using a packet-based routing system. However, it doesn't always achieve the low latency and reliability of a telephone call. Of course, if someone has more experience with these types of networks I'd be happy to hear more.