Plessy v. Ferguson was overturned because folks came to see it as bad law. And well it should have been overturned. Roe v. Wade should meet the same fate.
"Separate but equal" sounded good in theory, better than the alternative of "nothing at all". Segregated schools were better than no schools at all. Separate water fountains were better than none at all. "Colored" seating in a movie theater were better than no seats at all. A "colored " takeout window at a restaurant that would never allow blacks to dine was better than no chance to get a meal from the restaurant. "Separate" neighborhoods may have been slums, but those were better than no housing whatsoever.
"Separate but equal" proved to be an oxymoron in practice. American law may not always be rational in result, but it tends toward a chilly logic. Roughly sixty years after
Plessy v. Ferguson, the "but equal" segment of the phrase had proved impossible to realize reliably. Note also that in the 1950s, Americans had come to recognize that the segregation of people based on something not so obvious as skin color (like the religion of one's grandparents) had served as a pretext for one of the most horrific crimes of history.
Had segregated facilities and institutions proved to have at least the potential of offering equality of result, then
Plessy v. Ferguson might have remained intact. But in practice blacks almost every where and some Asian groups in the West clearly got worse -- the cast-offs that the white community was willing to offer.