Meanwhile, borders are required by nature, because cultures are not interchangeable and cultural friction exists, rendering borders and controlled assimilation necessary.

You also committed a logical fallacy:

> No person is illegal as borders are arbitrary

That's fallacious. All laws are arbitrary, as the GP pointed out, and you somehow failed to read:

> Speed limits are also arbitrary, enforced by other humans

So, it's factually true that borders are both necessary due to nature, and exist in the legal realm such that "illegal immigrants" is a factually correct label.