Two somewhat unique American laws combine to create our totally stymied immigration situation. The first is that under US law all who arrive on our shores are considered to be immigrants, unless they prove that they are temporary visitors, usually shown by the visa under which one arrives. As far as I have been able to determine no other country uses this formula and, if there are, they are few and far between. In any other country arrivals from abroad are considered to be temporary visitors until they should ask to be an immigrant. Thus in most countries the authorities simply eject foreign visitors for whatever reason they have. However, since all arrivals in the USA are considered to be immigrants, they have the law to protect them from removal.
The other U.S. law that serves here is that used to determine citizenship. Countries use two rules for this, birth in the country or parentage or, in the USA, both. I have two daughters born in other countries. Neither has a claim to citizenship in those countries since the law in both state citizenship is transferred to children from their parents. This can be transferred from the mother, the father or both.
The majority of countries use the parentage formula for conferring citizenship. Some, as the USA, use both parentage and birthplace. I know of no country that only uses place of birth for conferring citizenship. I do know that Latvia confers citizenship to anyone who can speak its language which has to do with denying citizenship to the many Russians who remained there after the fall of the “Soviet Bloc.”
If we are really serious about cutting the “Gordian Knot” that is our present immigration system, we should start by reviewing our basic laws controlling the admission of foreigners into our country and the conferring of citizenship. Perhaps the USA could benefit by conforming to more widespread practices among the nations of the world.