Having an essay essentially written for you by an expensive consultant with contacts in admissions departments is undetectable and widely practiced. But when it comes to standardized tests, many wealthy families get so desperate for good scores for their kids that they engage in criminal conspiracy (recall the Varsity Blues scandal in 2019).
It's extremely hard for me to see how, when you remove the least gameable aspect of admissions, that it gives the rich less of an advantage. I'm almost certain it gives them more of an advantage instead.