There are several use cases. But the main reason is always to operate in a situation where the number of tests is a bottleneck or constraint. In the USA, this is usually because of limited test reagents or limited laboratory techs and machines to run the PCR.
If you have unlimited testing, you would not use pooled testing.
One use case is surveillance. You ...
The principal goal of pooled testing is to rapidly clear many cases in low prevalence (or incidence) situations.
Disclaimer: I'm analytical chemist, i.e. someone who could by profession be involved in developing such tests, but I'm not involved in SARS-CoV2 testing or SARS-CoV2 test development. What I write here is basically my general ...
Group testing was introduced by Robert Dorfman during WWII to "weed out all syphilitic men":
Robert Dorfman, The detection of defective members of large populations, Annals of Mathematical Statistics, Volume 14, Number 4, 1943.