Is that generally true or is that a stereotype?
Legacy students also had a higher average SAT score than non-legacy students, at 1523 for legacy students and 1491 for non-legacy students.[1]
[1]: https://www.thecrimson.com/article/2021/9/8/2025-freshman-su...
Now, a few guesses: first, to the extent that affirmative action is even partially successful in targeting disadvantaged groups, affirmative action students should be less likely to be legacy, meaning that applications of legacy students should at least reflect a numerical superiority consistent with the strength of the affirmative action bias. Second, I will say that from personal experience I valued, more highly than was deserved, the schools that my parents attended; in this way those schools were the beneficiaries of highly effective advertising, through my parents, that made me more focused on those particular schools than they deserved (so much so that two of the three were two of the four schools I intended to apply to.) The aggregate outcome of that effect across all legacy applicants should be a higher-than-usual applicant quality in the pool of legacy students.
Would the legacies tend to have much higher income, or is any old person who's a child of an alumnus considered a legacy?
This is the arbitrage opportunity for lower-ability legacy students. If the schools provided elite educations, they would chew up and spit out lazy rich kids (and probably generate parental acrimony toward the schools in the process, weakening the donor connections.) As affirmative action of all shapes and sizes creates an ever-expanding group of people most likely to fail who the school is particularly determined to not flunk, there is more safe space for deadweight rich kids (which, for the record, I suspect is an overplayed trope relative to actual prevalance, though probably not hard to find at top-ranked schools.)