It really boils down to which of the two is more expensive: giving the vaccine to people who already have had it or giving a test to everybody and the vaccine

It really boils down to which of the two is more expensive: giving the vaccine to people who already have had it or giving a test to everybody and the vaccine to people who don't pass the test. It's worth noting that the tests are slightly inaccurate, so a test+vaccine strategy would also fail to vaccinate people who return a false positive on the test. If the vaccine manufacturing supply is not constrained, the capacity for running tests is much lower than the capacity for vaccinating. (Test requires a machine and between 15min for rapid and O(hours) for PCR.) Giving a vaccine is somewhere between one and five minutes per person. (Paperwork, clean site, inject, bandaid, next.) Plus vaccination is much cheaper to scale out -- you just need a few chairs and a folding table and a volunteer to create a flu vaccination station, for example.