That is an interesting why of handling it. It would also solve many other problems.
In my simple mind we don’t even need to go that far. Our existing law already provides that we don’t have to give citizenship to those born her who are not subject to US jurisdiction. From the 14th Amendment - “persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States.” Illegal aliens are not subject to our jurisdiction, therefore their children born here are not citizens. IANAL of course, and I am sure that many parties with interests other than those of the citizens of the United States would work very hard to find a way to prevent such a legal interpretation. They are not just wrong to do so, but traitorous IMAO.