The issue is that many Republican voter ID laws are designed explicitly to discriminate against non-white voters by requiring ID they frequently don't have and would need to bend over backwards to get.
In many cases, the GOP mandates photo IDs because they know a disproportionately larger number of black people won't have examples of these on hand, like driver's licenses. They may issue dedicated voter ID cards if you don't have those, but they also intentionally make it difficult to get those cards (such as by closing offices near black communities). The result: some black people may not end up voting simply because they don't have hours to travel across town and wait in line in the middle of a work week.
Proof of identity is fine, but the standard doesn't have to be nearly as exclusive as Republicans make it. Utility bills, bank statements and many more items qualify.