I spent a summer looking over cases where people are being removed/deported and I have to say that the 14 Amendment and immigration law are not very compatiable. A driving factor in US immigration law is family unification, but the 14th Amendment works counter to that policy because parents and children now have different nationalities
The 14th amendment also provides a pretty significant and permanent loophole for many undocumented aliens. Undocumented parents can apply for cancellation of removal if they are ever deported based on hardship to the US citizen kids. Once the kids are in grade-school the judge usually lets the parents stay unless the parents have criminal records. Eventually, once one of the kids turn 21, the parent can immediately apply for a greencard.
I think it makes more sense to give the children born in the United States the same legal immigration status as their parents (perhaps their mother since that’s easiest to prove).