How do you identify race? After all, it's just a social construct. We're not DNA testing and doing the one-drop rule are we? Its' self-reported. At least with socioeconomics we can look at household income and tax returns.
It's definitely a thorny process whichever factor one adopts to benchmark process outcomes against.
Meanwhile, everybody pays taxes so we have the data we need to not use racial discrimination.
Actually, the very wealthy _don't_ pay a ton in taxes, depending on how their wealth is invested and distributed.
What wealthy folks often do is to take lending against their assets, giving them liquidity. This is not taxable income.