Depending if those problem are true or not for any given state, but if they are then those issue represent a major problem beyond that of voting.

To take a example from Europe, membership cards from schools/universities, banks, and driving license work as automatic identity cards. For those who neither study, have a bank account or drive then the police should provide one. For the wast majority this mean that ID cards are automatic process of normal life, and for the rest it is a simple matter of requesting one at the nearest police station. As a result almost everyone has some form of identification card or an other.

It can definitely indicate a major problem beyond that of voting.

But what does that have to do with voting? Should they have a harder time voting because they already have other major problems anyway?

Had to think about it for a while, but I think you answered the question accidentally. It does not have anything to do with voting.

Lets imagine we had a state which got tired of vulnerable and weak social security number. In every place where it is used we replace it a two factor hardware token that include bio-metric data (a photo), issued by the government or institutions like banks that by law are required to follow strict requirement of identification. I think we can both agree that this initiative would not have the goal to make voting harder, nor prevent voting fraud, but rather fix identity theft caused by the weak password-like system of social security numbers.