The reason is purely political. Even if a politician wanted to do it (It was something that Donald Trump campaigned on), it is very controversial matter, and every major news outlet in the country (POSSIBLY excepting Fox News) would immediately brand the sponsor(s) of such legislation bigots, xenophobes, flat-earthers and anything else they could think of.
Despite Leftist assertions to the contrary, the Fourteenth Amendment DOES NOT sanction birthright citizenship, and in fact there are no Supreme Court opinions on point. Hence it could easily be eliminated by Congress with appropriate legislation. It would take a Republican Congress and President to pull it off, and it would probably have to EXCLUDE anyone who was born in the U.S. prior to enactment of the law.
The following text comes from the Fourteenth Amendment:
"All persons born... in the United States, and subject to the jurisdiction thereof, are citizens of the United States..." The words, "subject to the jurisdiction thereof" were intended to exclude the children of foreign diplomats. Leftists simply gloss over those words and deem them meaningless. But they apply directly to children of illegals who are - ta daa! - subject to the jurisdiction of their parents' home country.