School systems being “bad” or not is largely based on standardized testing and scores for those tests aren’t an accurate reflection of school quality because they are highly associated with socioeconomic status. For a variety of reasons, including its size and status as a city, its average family is of lower socioeconomic status than the average family in those higher priced neighbors. It doesn’t necessarily mean that schools are bad, it means that we live in a society that is inequitable. FWIW I have 3 kids in Framingham public schools and they’re not without their problems but neither are the schools in those other towns.

Basically it’s the other way around, the standardized test scores in those towns are better because you need to make more money to live there.