In reality, the lack of level playing field comes from cultural capital. Americans see standardized testing as beneath them and don’t prepare for it. When my uncle came to America, he moved with his wife and two adult kids into a tiny 2BR apartment in a shitty part of Queens. But I’m sure they scrounged together the $1,500 for my cousin to prep for her GRE. Meanwhile, despite extensive prodding, my wife couldn’t get her younger siblings to study for the SAT. Both were much better of economically than my cousin, and could definitely afford a prep course, they just didn’t do it.
It’s not clear to me what you can do to level the playing field in a way that’s actually fair. If you don’t have the cultural capital to know to study for a test, you sure as hell don’t have the cultural capital to know how to stand out in an admissions process based on soft factors. I spend $30,000 per year per kid to send my kids to a private school with old money Annapolis WASPs, precisely so they can get access to that cultural capital. It’s a terrible idea to make that sort of capital more important by reducing the emphasis on objective factors.