There is no universal right to immigrate to the US, or anywhere else generally, so immigrants can be subject to whatever requirements the local govt decides at any given time. The discussion here was about a supposed "free travel" zone where citizens of member countries are giving up much of their autonomy in return for travel and trade freedoms.

But this kind of arguments are precisely the point when it comes to concern about precedents. It becomes less of a barrier to adding new rules just because the law already has vaguely similar rules.