It's important to note that the idea that Roe was decided incorrectly, is a myth perpetuated by fedsoc and other reactionaries. And the liberal legal academics did nothing to counter it.
Do you really think they wouldn't still overturn if it was decided based on equal protection? We should not fall into the trap of deifying the court. They are not above politics and they never have been.
And they didn't rule against it because of the privacy angle. They ruled against it because they are trying to destroy the jurisprudence of substantive due process and unenumerated rights, because it serves their reactionary politics.
Only if you buy in to the reactionary attack on substantive due process in general. And it's a mistake to think if Roe were decided any other way, that it still wouldn't have been overturned. Reactionaries do a great job of smuggling their politics as socially acceptable, fictional legal frameworks like textualism, even though they clearly abandon that whenever it is in conflict with their politics.
https://www.newsweek.com/ruth-bader-ginsburg-roe-wade-aborti...
https://www.law.uchicago.edu/news/justice-ruth-bader-ginsbur...
https://www.washingtonpost.com/history/2022/05/06/ruth-bader...
Seems to me RGB did feel that ruling was weak and should have decided based on equal protections not privacy.