I think your question is a fair one. Most schools are quite excited about enrolling middle class kids, but for some of them, it can be hard to be among kids with significantly more wealth and who often have other ties to each other pre-BS. Generally not to the point that they have a miserable experience but they can feel a bit on the fringe. And some kids won’t register this at all.
Schools that offer FA to at least half their students may be ones less dominated by this. Westtown, George, and Mercersburg are 3 that fit the bill by that measure.
It also helps if a student has other ways of being part of the community, such as sports or theater. The “fringe” feeling can disappear quite quickly if you’re part of something else.
I’d find schools that look like a good fit in terms of interests, etc then do a little more in depth digging on the overall vibe. This concern should not discourage you from finding a good BS opportunity for your D.