As someone who's somewhat ambivalent about race-based affirmative action (in short, I feel it's oversold at elite institutions and underused elsewhere) - a widespread adoption of something like this seems like an improvement over the status quo from the perspective of fairness. With that said, I don't think it will end up being used in this manner because fundamentally institutions are indifferent to your hardship and generally want the least fair process possible. At least as far as you can infer from their actions, top schools don't want students that overcame hardships. They want students that are likely to be successful. And given equal test scores, those that overcame more hardships are probably less likely to be successful, since they are likely to face more difficulties and less support in the future.

For example, if Harvard admitted purely by academics (assuming that a suitably hard version of SAT exists), they'd certainly have a student body that overcame more adversity they currently do. But they'd miss out on the likes of Jared Kushner who, despite low test scores, certainly had better career prospects than the average Harvard student. In reality top schools are generally looking for well-bred, well-rounded rich kids that are going to be successful no matter what. Everything about their process optimizes for this - relatively easy tests and low cutoffs, focus on extra-curricular and well-roundedness in general, ridiculous emphasis on sports no one without money would play, legacy preference, the list goes on. Admissions officers are even known to prefer more expensive extra-curricular activities - it's not about ability, it's not about effort, it's about interestingness and rarity, which are essentially synonymous with expensive.

Then to mask the fact that this is what their admissions process optimizes for, they just put the lipstick on the pig to make the result superficially palatable. This is where race-based affirmative action comes in - the whole holistic admissions process is fairly blatantly regressive, but somehow it's sold as a package deal with race-based affirmative action (it doesn't have to be) to put the critics on the defensive, as though they are the ones defending privilege. It's a fairly brilliant rhetorical technique, I must say. The holistic admissions process is primarily used to admit rich kids who aren't quite good enough academically over middle-class/poor kids who are great academically, but just have a hard time distinguishing themselves due to their chea, extra-curriculars that are available to far too many people to be interesting. But the fact that this process, combined with race-based affirmative action, yields a few more upper-middle class African immigrants and far fewer poor white and Asian kids, is apparently enough to give them the moral high ground.

They've done such an amazing job pushing this narrative that most people seem to think rich kids getting SAT tutoring is a big problem from a privilege perspective and de-emphasizing objective metrics is about leveling the playing field. It's the exact opposite - they want every excuse to admit the people that they think are going to be successful (and what better predicts success than growing up already successful?) and de-emphasizing objective metrics allows them to fill the entire class with mostly privileged people, without the riff-raffs that are academically good, but don't have the connections or the upbringing or the money to be successful.