"The EU" can't enforce this list to member states - it's up to each government to act. it also can't "reinstate stricter borders" - EU is not a government.

It's not surprising that countries want to avoid travelers from infected countries though. There are already tourists with infection that tried to "sneak in" to the south by traveling through germany for example.

Going forward, containment a-la new zealand seems to be the most viable economically solution for reopening, even if tourism is gone for a year or two.