What is a main problem with basing affirmative action on class rather than race?

class can be more easily faked than race

Explanation:

Let's say that we put affirmative action based on class and will provide more opportunities to enter universities for the family with less than $20,000 income. (pretty much within the poverty line).

University workers have to conduct an identification to prove whether the people who apply actually met such criteria. If the affirmation is based on race, it will be really easy to verify the applicants (just take a look at their IDs)

But, if the affirmation is based on class, the Workers have to make further efforts to prove by investigating the applicants one by one. They have to collect proof of income, take a look at their houses, making sure that they do not do anything to hide additional income, etc. All of these things need to be done to ensure that applicants do not fake their class.