It is not that easy. Even though I got my 2. shot Pfizer today, and even though EU has an idea of a "corona passport" letting all EU citizens travel freely if they have this corona passport, then real life looks different. EU can't really agree on anything which is why it is a circus to find out where I CAN go. There are lots of local rules overruling EU's idea of free movement. Borders has been closed since 2015 and corona has not made them more open.
Not even agreeing on which countries are "dangerous" are EU able to be.
I can understand, that UK citizens are allowed to travel to Antarktis?
I cross borders every day living in Sweden, working in Denmark, and the last year has been a living hell when it comes to crossing borders.