I'm genuinely curious to know if scores-only admission would deliver a more economically-diverse student population. I don't know how you'd investigate that though.
My hypothesis is, if there's no benefit to doing expensive extracurricular activities, hiring a personal essay coach or college counselors, getting recommendation letters, and all the other ceremony, elite colleges might become more accessible to students of limited means. There's only so much of an advantage that expensive test coaching can give you, right?