Logistics & Economy
Medical tests require:
- Qualified crews.
Checking a document require a few seconds time of an entry level clerk.
Medical tests are way more expensive and disruptive than checking documents, and they escalate poorly.
I happen to be closely involved in the procedures for handling passengers at a local airport. Although they were advised to come with a PCR test results, those who did not have one would be subjected to an antibodies test.
And even with only a fraction of the passage affected, and with travel severely curtailed, it has already been a difficult task. You have to receive all the passengers, sort out who needs the tests, administer the tests, wait for the results, communicate them to the waiting passengers (and beware of privacy issues), getting sure that no passengers leave the testing area before getting the results...
If you want to allow travel on a significant basis, you just cannot rely on performing medical tests on arrival. It simply does not work. So you settle for the best next: assume that vaccinated people won't get infected, and let them pass freely.
Yes we do know that some vaccinated people may be infected and contagious, but even the risk of those who can be reinfected depends of the infection rate at their origin. So with low rates the governments are willing to bet on easing the restrictions on travel in order to estimulate the economy and appease the public. There is certainly an element of risk (as there has been any time restrictions have been eased) but they seem to expect to contain the situation at least until vaccination is high enough.
It is not that different from the current situation: even PCRs leave some room for not detecting infected people, yet may EU countries allow travel without quarantine with just a PCR. There is a need to balance the costs and risks of each safety measure.