These tests are specific for SARS-Cov-2 but I agree there is a high false negative proportion. Their usefulness is in reducing the quarantine time. So 1 negative test and 9 days quarantine is as good as 14 days quarantine. Two PCR tests and you can reduce it to about 5 days
However quarantine, checking temperature and symptoms, and PCR tests merely pick up a proportion of infectious passengers. So if people are coming from areas with very high levels of infection they still are not adequate
The antibody test however is very cheap and has high specificity, and if you are positive you are not infectious - we havent seen a single case of a patient being infected twice - each and every such claim has been discredited. Although the antibodies only last 78 days we know it is normal for antibodies to disappear with time but immunity to continue, but in some hospitals we just bypass that concern by retesting
So the sensible thing to do would be to give an antibody passport for the 13% of people who are safe, and then do 2 antigen tests and 5 days isolation for the others
A vaccine is coming. This is a simple piece of RNA that has only mutated once and the P1 and P2 studies in many different vaccine trials have shown they can produce good antibodies and good T lymphocytes. I wouldnt put my money on any particular vaccine but I would put money on one or more working.