When they are residing and living in the United States, they are under and subject to all of our laws....NOT their country's laws....they are fully subject to every law in the USA, and are given every protection of that law, and also every protection from that law... with things like due process, Miranda rights, 5th amendment, habeas corpus, right to a speedy trial, etc. in at minimum in criminal cases.
Under common law, jus soli, and before this amendment, anyone born on our soil, had U.S. citizenship...IF they were not one of the three exceptions mentioned....
and of course slaves were an exception. The 14th basically said, under all conditions other folks who had kids born here are citizens, black folks kids born here, and any nationality or skin color of the persons here, their children are citizens too, if born on our soil. Jus Soli.
Good read:
en.m.wikipedia.org
I really think, there is no way around the amendment's clear language and in order to change it, can't be done by pretending the words didn't mean what the words simply said in the amendment, and will need an amendment to change it.