All three of my nephews and nieces were the products of birth tourism. They are not white, they are Asian.
Your point makes no sense. My brother-in-law is a wealthy Asian and he wanted to make sure his wife had access to high quality American health care because of the risk's related to her pregnancy. Citizenship was a bonus, but health care was critical, his wife's pregnancies were "high risk".
So, how are three Asian babies a form of white privilege? Many Africans travel to South Africa or Europe to have medical procedures because of the quality of health care available.
Hint these Africans are "black". So, are you saying this form of medical tourism is a form of "black privilege". The links below may help you understand medical tourism better.
If you want to argue the wealthy have access to better health care, then make that argument. It is better to be rich than poor and rich comes in every skin color.
https://atwconnect.com/top-4-african-medical-tourism-destinations/
https://medtoursafrica.com/why-do-africans-prefer-to-have-medical-treatment-abroad/#:~:text=So%2C%20to%20avoid%20taking%20a%20gamble%20on%20their,Middle%20East%2C%20Western%20Europe%20and%20the%20United%20States.