"Zero work visas" leads to even more egregiously stupid outcomes. No trade shows. No touring bands.
("Zero immigration" also means that if one of your nationals wants to marry a foreigner, they have to leave the country. And so on.)
(I do get that there are justifications given that framing...)
Here's a more forthright approach: The problem with your argument is that it goes about half a level deep and doesn't hold up to even the most elementary criticism. Specifically, I was pointing out that human constructs are a fundamental element of human existence; they are how we negotiate existing alongside one another. So, trying to argue against something solely because it is a human construct makes about as much sense as arguing that somebody is evil because they were born in February.
The notion of real border control is barely 100 years old.