ferries, channel tunnel, trains, automobiles, nope, just won't do... I have driven from London to Athens in less time than many of these people have been sat in airports wringing their hands... I also suspect that it may be CHEAPER to hire a car and drive back home, than to attempt to live in an airport for a week.
I guess you haven't been reading the stores about the Eurostar and the ferry companies having their busiest days ever. Or the thousand euro taxi rides many are resorting through. Have you considered that people would like to get a train or ferry but they're all booked up?
In a universal care system, the government can mandate that only tests X, Y and Z may be performed for symptoms A and B, or that test X is only done once per year with as long as no symptoms are present.
Then that applies to a universal insurance system. And universal insurance is a type of universal healthcare anyway.