I would imagine the socialization benefits of family income probably massively enhance interview skill and (even more) letters of recommendation as well, no? And for the essay, this seems easiest to fix with wealth as you can hire someone to either write it for you or massively edit it and assist you with it.
Any time someone proposes to get rid of this or that requirement for being correlated to wealth, I'd like to see what the alternative is and see if it's any better.
We want something somewhat meritocratic, where we can tell the difference between natural capability and hard work on the one hand and simply being lucky to be born into wealth on the other... but it's not clear to me that objective measures like the SAT are going to be worse than interviews/letters-of-rec/essays in discerning that.
I've also read SAT scores are highly correlated to family income. Family income probably has a huge impact on post university outcomes.