If the borders were completely open then it is likely this system would collapse or perhaps be forced to introduce the idea of "second class" citizens with tiered benefits.
It's possible this might not happen but as far as I know the experiment has never really been tried.
There's a lot more to nations than just "land and freedom of movement". There's a regulatory climate, political system, local culture(s), defence, social contracts. It feels to me a bit like you are handwaving away all the "hard" parts of being a nation.
The half-way solution is to restrict immigration those who can demonstrate they'll contribute and not be a drain on locals (i.e, not divert too much resource away from existing citizens who currently benefit from and support the system). It's very divisive and a compromise that leaves many unhappy. Interested in your thoughts on balancing universal benefits with open borders.
Housing prices in e.g. Zürich and the surrounding area are already insane. There's something fundamentally sad about being priced out of the place you grew up in, let alone the country.