Bravo Rubio
The administration might not be able to ban birth tourism, but that doesn’t mean it’s powerless against it.
For example, there’s this:
The State Department’s new policy uses powers under the Immigration and Nationality Act to yank visas from those “who knowingly engage in, have engaged in, or facilitate birth tourism to the United States,” including so-called visa fixers, or individuals who coach foreigners on ways to lie or exploit America’s immigration laws.
The US has long maintained a set of rules intended to prevent birth tourism.
The words “a set of rules” links to this article dated January 23, 2020, written at the beginning of the final year of Trump’s first term as president. This tidbit of information is of interest:
Chinese citizens do not require a visa to visit certain U.S. territories, such as the Commonwealth of the Northern Marianas Islands. The birth tourism industry is rampant there, with more annual births to Chinese visitors than native residents.
Birthright citizenship tends to be organized by those who make money off it, so this move against them is an excellent idea.

Perhaps another way to address birth tourism is to appeal to Xi’s national pride. IOW, to suggest that Chinese expectant mothers should demonstrate their pride in their own country by giving birth in China — not in another country. Would that work? Not at first, but if that theme were played insistently enough, perhaps Xi would be responsive to it. And if Xi say no, that will mean no for a lot of Chinese. Even the wealthy ones.