I don't think birthright citizenship qualifies as a "human right" - most countries that (officially) care more about "human rights" than USA does doesn't have that. Whether it should be removed or not is not for me to say, however. It's a switch away from what it has genuinely mesnt to be an American.
Not having birthright citizenship doesn't (necesarilly) mean the newborn wouldn't have any citizenship at all
Don't forget the millions of Poles