WI does have free ID that is acceptable for voting. However, it's at the DMV, which has limited hours and as previously mentioned, it's often difficult for poor minorities to get there and also have the appropriate paperwork on hand.
In addition, my husband, who has a perfectly acceptable ID for voting, was initially turned away because his printed driver's license address didn't match his voter's registration. We moved recently, and WI allows you to update your driver's license without printing a new one, which is the option we opted for.
However, the picture ID is not to determine your address, it is to determine your identity. He was turned away in error. Luckily I had already voted and he knew this (and we both came with proof of address as well), so he pushed to get the issue resolved and was able to vote after talking to a supervisor. However, this makes me wonder how many other eligible voters were turned away in similar situations and didn't press the issue? Again, minority and poor urban folks are more likely to have moved without updating or printing a new driver's license. So even though their ID was appropriate for voting, uninformed poll workers could have turned them away.
In addition, one of our congressmen
openly admitted that voter ID laws help the GOP.
The difference between Hillary and Trump in Wisconsin was about 27k votes. If this study is correct (and my guess is that it under-estimates, rather than over-estimates) it's very possible that the results could have been much closer, if not reversed, without this law. Of course, not all the prevented votes would be for Clinton, but the majority likely would have been.