Do you carry your birth certificate with you because you needed it to get your passport?
The ID at voting is supposed to confirm that the person is a particular registered voter. If they are not allowed to vote then they would not be registered.
I do agree that people would feel more comfortable about the voting system if voters produced a physical object rather than the current scheme of saying a name that is registered and they can assume nobody else will say. If they allowed a few obvious things like Student ID's or utility bills the number of disenfranchised voters would be small enough that it would not effect the voting results (it would not be zero though so there will always be sob stories for opponents of ID). Crossing names off in a register is still going to be done since that is the real prevention of fraud (including stolen IDs), but public comfort even if it can be proven that the IDs do nothing can be considered a useful goal.
The Republican attacks on the ability to register to vote are pretty serious. IMHO anything done by the government that happens to know if you are eligible to vote should automatically register you, in particular getting a RealID drivers license, and quite a few methods of applying for benefits. The attacks on mail-in voting are also blatant, mail-in votes are a good deal more secure than any non-biometric ID since they require the voter to have access to the mailbox that the numbered ballot is delivered to. I also personally know I will be out of the country on Election Day so I am personally disenfranchised by this. The continuous claim that the only thing in that bill is ID at voting is a LIE, stop doing it.