I don't inherently agree with that line of reasoning either. There is a severe caveat to that, however.
In some states, IDs are (without paperwork and bureaucratic wrangling) between 3-10 dollars. I think this is an acceptable amount of money to pay for the ID. The problem I have with it is that many states have much more expensive IDs. Now, many of those will design free or discount IDs, but that is a more complicated process for many folks, and is not simply bing bang, done.
Now, in my state, IDs are $6. Up until this latest push by my legislature (who is pursuing this for little practical reason), we did not require ID cards in the slightest. Now, in North Dakota there is no voter registration and there is no ID card requirement. For the sake of convenience, voters are asked to pull out their IDs, and a vast majority do. A voter could use an assortment of resources to vote, including a utility bill. If you are not on the list of previous voters, your information is written in a quick few boxes by the staff, and away you go. If you have neither the information nor an ID, a staff member can vouch for you if they claim they can give assurance.
Despite all of the fervor as of late by the legislature, I cannot recall a single news story about the incredible need to protect our vote in the state of North Dakota.