They just can no longer make it obvious that they are admitting a student on the basis of being an ancestor of a former student.
Similar to what real estate professionals and hiring managers did following affirmative action, admissions departments will just find and cite circumstantial merit based reasons for admitting such students when they're still essentially legacy admissions.
The only rich kid legacy students who will legitimately get shut out are the bad unqualified HS students who don't play a sport.