Don't forget there is a chance of a false positive test result, so even if you have yourself tested before you travel, get a negative result, and don't develop coronavirus en route then you may still get a postive test result on arrival. Since insurance is unlikely to cover this event, you must be prepared for these losses yourself.

From https://arc-w.nihr.ac.uk/news/corona...navirus-tests/

You can see that in this example, if most people don't have coronavirus the number of false positives compared to the number of people with coronavirus is quite high. This is always a problem with a low-prevalence condition and an imperfect test (compare the amount of people actually trying to breach airport security compared with those who are suspected to be doing so erroneously, and so on). All biological tests are imperfect to some degree.
Hopefully re-testing is an option for the several percent of false positives.

The problem of false negatives gets a lot of press. The problem of false positives gets much less publicity, but when we are talking about detaining someone against their will for 14 days then accuracy is important. We would consider a case of mistaken identity leading to Police arrest and detention for 14 days to be a problem, and we should consider detaining someone for another false reason to be problem too.