[fluffything]

> so it's hard to disentangle or fix

Give the Id to everybody who wants it for free. If someone cannot prove citizenship, but they can prove having worked or lived in the US for more than 5 years (checks, bank receipts, etc.), give them citizenship.

There, problem solved. That way, you only discriminate against those who are either in the US illegally and are not working, or are working but have been illegally living in the US for less than 5 years, and both situations are fixable by the individuals themselves (work for 5 years and "earn" your citizenship).

Of course, what many want is an Id that can actually be used to prevent poor people from voting, while also being able to employ those same poor people at very low rates using the fear of "reporting them".