I can tell you what I wanted for my oldest. I wanted him to be at a place where he wasn’t always the smartest kid in the room. Where he’d be challenged and have to work hard for the first time in his life. Since he turned down a college that is generally rate one or two for one that is rated in the 20s I don’t consider myself obsessed by prestige, but I do believe prestige has its place. I’ve gotten at least two jobs solely based on the name recognition of my undergrad college.
And the DC schools are notoriously terrible. Everyone I knew in public junior high went to private schools or their parents moved to the suburbs. I don’t think much as changed in the intervening years sadly. It’s not a bout the prestige of the prep schools - it’s getting a decent education.