Also, the freedom of movement is not a blanket statement. It does not, for instance, grant me permission to move into your house.
Socialists are not coming for your toothbrush. We ask for a world in which people are free to live and work where they please. A world where people are not thrown in cages or separated from their families because they cross an invisible line. We don't need to walk into your personal space to have that, but if we did for some reason, hi, how are you doing? :)
Maybe block known criminals and bad actors, but otherwise yes. If your argument as to why we should exclude people is based on the idea that it would make standards of living worse for people here, that's a) probably not true and b) only makes sense if you think the wellbeing of the people here is more important the wellbeing of people elsewhere.
>It seems like that nullifies the existence of the nation itself. Why have a border?
Not really, there'd still be a government and a system of laws that apply within the border.
But beyond that, why specifically do you think it would be bad to nullify the existence of a nation?
>Why have a military to protect that border?
In as far as a military is necessary, it is to protect against other militaries, not non-violent civilians entering the country.
EDIT: Also, our institutions have been shown by recent history to be a complete farce. Maybe new people would rebuild them better without the taint of authoritarianism, hierarchy, and corruption.