Packet switching won over circuit switching because the cost-per-capacity was so much lower; if you have to end up over-provision/under-utilize links anyways, why not use circuit switching?
It's common knowledge to run your API nodes at 20%-60% CPU load, no more, exactly to curb tail latency.
You can deploy a 24-fiber optical cable and allow many thousand virtual circuits to run on it in parallel using packet switching. Usually orders of magnitude more when they share bandwidth opportunistically, because the streams of packets are not constant intensity.
Running thousands of separate fibers / wires would be much more expensive, and having thousands of narrow-band splitters / transcievers, also massively expensive. Phone networks have tried that all, and gladly jumped off the physical circuits ship as soon as they could.
Both are technologies that one rarely has any contact with as an end user.
Sources: Things I've read a long time ago + Wikipedia for ATM, Wikipedia for MPLS.
This was undoubtedly true (and not even close) 20 years ago. As technology changes, it can be worth revisiting some of these axioms to see if they still hold. Since virtual circuits require smart switches for the entire shared path, there are literal network effects making it hard to adopt.