The rapid antigen tests have a significant problem with false-negatives: the BMJ reported that Innova tests have 49% sensitivity.
That makes it pointless to use as a border control - for every two cases, at least one gets through. (Or, potentially much worse, under this system: I throw away my positive tests and show whatever false negative one I have).
You ideally want to be conservative and permit some false positives at an effective border control, because you don't want to risk infectious cases getting through and causing an untraceable national breakout.
Even tiny sensitivity would be better than nothing – or something that's so slow & expensive it's impractical.
But other antigen tests purport to have 90%+ sensitivity.
And the kinds of "PCR positives" they miss are often cases that are no longer infectious, anyway: lingering viral fragments, rather than live full-virus shedding.
So: ideal for border-control & creating other internal gradients that help suppress the worst active cases. The perfect should not be the enemy of the very good.
> Even tiny sensitivity would be better than nothing
Not if you imagine that one case on a plane = potential super-spreading event, the plane touches down and then newly infected people go in every direction.
Your hypothetical test with tiny sensitivity is pointless, in this regard: it has a (less than) tiny chance of preventing each risky passenger. In my view, any kind of low-sensitivity testing before departure is theatre: it won't make any difference in preventing new infection from breaking out.
The government of the country that I am in agrees, and requires a negative PCR test.
That makes it pointless to use as a border control - for every two cases, at least one gets through. (Or, potentially much worse, under this system: I throw away my positive tests and show whatever false negative one I have).
You ideally want to be conservative and permit some false positives at an effective border control, because you don't want to risk infectious cases getting through and causing an untraceable national breakout.