the problem is what better idea do you have? the idea of favoring "holistic student" just selects for students who have the time, money, and parental support to juggle 2-3 extracurriculars
in addition to sustained effort in classwork.
it's goodhart's law in action: any measure that becomes a target will cease to become effective. for any metric you choose, a wealthy student will be able to deploy their familial resources to fiddle the metric, because that's literally what money is - "stored power and influence". My stored influence allows a pizza to appear at my door or a lawyer to appear to defend me, and it makes a violin and a tutor appear for your kids, if that's what the metric becomes. Wealthy families will always be able to fiddle something.
The dirty truth is that a small, fixed, standardized exam is actually not a bad solution to that problem. Things that require sustained effort (grades) actually tend to bias towards wealthy families, as do extracurriculars and other "holistic metrics". Wealth buys all of those things. But getting a smart kid through a standardized test successfully actually is a much smaller, more equitable hurdle. The unpopular answer is that ultimately pretty much anyone short of the completely destitute can afford a couple hundred bucks for a month of test prep (and the book alone gets you most of the way there), and in the cases where that's not true it certainly isn't improved in those cases by requiring 6 years of violin lessons and 2 instruments etc.
I mean think of it like a job interview... is it really fair to ask the applicant to do a big take-home assignment that takes a couple nights to complete? Now imagine that you have to start preparing in middle school, and your parents have to provide financial support while you do it. We all have this intuitive sense as developers that a short, deep interview is probably better, and that a long convoluted process is neither fair to the applicant nor particularly useful due to false negatives/etc. And in fact for many positions there is likely a fairly low "good-enough" bar where anyone reasonably competent is probably gonna be fine even if they're not hyperspecialized in the exact thing you're looking for.
Honest question, if you are looking at this in the sense of "college as a hiring interview": if you want true equitability, isn't the best approach to "fizzbuzz and give an offer to anyone with no major red flags" (for whatever fizzbuzz/small task is appropriate for an interview question for your position)? Obviously college applications outnumber slots, but if you have 100k "qualified" applications for 25k slots, just give a slot to the top 10k and randomize acceptance for the other 15k? That kinda seems to be what people want for colleges, if you want a true "background-blind system" - cherrypick the best and then just give everyone else who has a reasonable chance of success an equal shot at admission.
Otherwise you do end up in these "well candidate X is 82.3% likely to graduate but candidate Y is 82.4% likely to graduate" scenarios and effectively you are making decisions inside the margin of error. And that is the point where your parents' money comes into play - even a small edge helps you in a decision that is made on these super marginal factors.