Why not?
You are correct, something could be done, but it would require amending the constitution. Maybe that could be done, but not anytime soon (and I still question whether it would get the support of 38 states).
14th Amendment, Section 1: All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside. No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.