Why not make laws to simply help the disadvantaged? Why does race have to be the indicator, even if its a pretty good one? Why cant income be the indicator? It seems like it would be at least as accurate, if not more so... and no need to bring race into it.
You suggest income, but then that ignores:
(a) debt
(b) medical costs (Joe & Jim have the same income, but Joe has cancer and has to pay $LOTS per month, has less energy etc. Who's more disadvantaged?)
(c) where one lives (Joe & Jim have same income, but Joe lives near where possible jobs are, Jim needs a 2 hour bus journey)
(d) existing assets (Jim has a new car and partner has a second hand car, Joe has a crappy car that could break, who is more advantaged)
(e) family support/obligations, both financial & emotional (Joe has to care for his mother, Jim's mother can pay for her own nursing home. Joe knows he can rely on his parents to bail him out, Joe can't). etc.
All systems have flaws. This stuff is hard and complicated, and you'll have mistakes, false positives and false negatives with all methods (yes including race/ethnicity). There'll also be costs to each method: Cost for the applicant to have to find & submit paperwork, cost for staff to process and review it, opportunities for fraud (e.g. asset-based-measurement means you can fake it by moving assets to a family member/close friend for a year).
Race/ethnicity has several advantages as a "disadvantage metric":
(a) easy to apply (hard to fake), yes there are problems with people of many ethnicities
(b) cheap and quick to decide, no calculations or hours of staff time checking that the payslip from 2007 is legit, or try to figure out if the person really is a single parent or is the partner still living there, etc.
(c) applicants don't have to find old information & forms & letters
(d) strongly statistically correlated with disadvantage
However some people just react negatively about race being mentioned at all, thinking that "racism = any reference to race" and "racism = bad" ergo "any reference to race = bad". Sometimes conversations about this can be like talking about evolution to a creationist, ask yourself if there is any evidence you'd accept that would convince you that it's OK to have affirmative action, if not, you might be being dogmatic.
The strong and convincing argument for affirmative action is that African Americans and Indians have been severely wronged in the past and should be recompensed.
But what about would Hispanics, more recently immigrants who never suffered from Genocide or Slavery.
Or what about Asian Americans, who actually suffer reverse AA (need higher scores than whites) for no reason other than being smart. They're aware of this and don't mark Asian on applications if it can be avoided.
Racial discrimination does cause problems. Personally, I really do feel that Blacks and Indians need to be compensated for past ills. I'm not sure how the best way to do that is, however.
Oh? Care to elaborate?
When I said "reduce paperwork", I mean it's less paperwork to evalulate and classify people based on race (since looking at a photo for 30 seconds will get you the answer 95% of the time (or some other high percentage)), vs. if you looked at income. To classify people based on income you have to look at lots of different forms and letters and statements etc.