You and I can rail about the interpretation of the 14th Amendment to the Constitution and speculate it on what it really means. However, we are not constitutional lawyers or scholars. We don't make or interpret the laws. The hard fact is that the current laws and their implementation by our legal system confers citizenship on people who are born here regardless of the citizenship of their parents. We cannot change this without changing the law and overturning a 100 years of legal precedents.
Or, quite simply, SCOTUS can rule that previous laws were not, in fact, in line with the Constitutional intent and overturn said laws that have allowed the children of illegal aliens benefits designated for American citizens. This type of correction of wrong/immoral interpretationwas done by SCOTUS in more cases than just Plessy v. Ferguson, 163 U.S. 537, which was overturned almost 60 years later by SCOTUS in Brown v. Board of Education347 U.S. 483 (1954).