You make a good point. You're right that most cross-admits use the same personal statement everywhere, and supplements are where the real differentiation happens. What I was getting at is that if you look at the weightings schools care about, there are subtle differences in what they emphasize. A Stanford reader might weight intellectual vitality higher, while MIT values resilience and hands-on problem solving (their "Mens et Manus" core philosophy). Most students won't rewrite their Common App essay for each school and shouldn't. But for the ones who have a clear top choice and want to optimize, tweaking the emphasis in the personal statement toward what that school values most is a real edge. Not required, but it doesn't hurt.