Are you not then essentially arguing that states have no sovereignty? If so, how far do you take it - do individuals? Can any migrant - legal or not - rock up to your house and start camping on your lawn?
Under the Svalbard Treaty of 1920, Svalbard is under Norwegian sovereignty. It is also an entirely visa-free zone. Anyone can go there, including same-day visa-free transit at Oslo Airport en route there. If someone lives there for 7 years they can then get Norwegian citizenship.
People can be deported from Svalbard if they are unable to support themselves or commit a crime, which I think answers your migrant topic.
FWIW, the Sovereign Military Order of Malta has no territory, and hence no borders, but has widely recognized sovereignty.
And, the distinction would be between public places and private places. Anybody is free to exist in any public place with no permission required (just like you are already allowed to do once you're in the country).
It would all be exactly the same as it is now, except there are no checks at the border, and no visa requirements.
I think it's utopian to believe that this would lead to anything but slums and shanty towns. People with no wealth will all flock to areas with wealth, which won't have the infrastructure to support them. They'd camp out wherever they could with whatever they could - possibly right outside your house. Probably in your back yard actually - local law enforcement would be too overwhelmed to go around persecuting squatting or trespassing.
Travel to a large city in India to see what happens when free movement is coupled with massive inequality.
People will find a way to keep people they don't want near by away from them.
1. if any person on earth could sleep in their bed, would they want to?
2. if they do want to, what circumstance are they in that that's something they would want?
i.e. if everyone has their own bed, why take yours
Obviously I'm simplifying and referring to an impossible utopia here, but the sentiment stands regardless. The point is, once you're taking it that far, both sides are absurd.