you have to ask, how are these countries going to open themselves up. A whole population with little to no exposure to the virus may not be the best strategy economically in the long run when the rest of the world has moved on.
Vaccinate their own population and demand proof of those arriving have been vaccinated. I expect in the early days of vaccination there will be no proof from the U.K. but then someone will cotton on when restrictions on U.K. citizens are not lifted.