This is a question that is highly dependent on culture, history and location. In Europe nobody would bat an eye and agree to that. But the US had malignant actors that tried to exclude people from voting that were not in their camp. It was nothing else than targeted discrimination. So being skeptical is completely warranted, even if you believe that the US has changed. And even then there can still be problems.
It has to do with lacking trust in today's institutions as well as towards the police.
A quick google search suggests that it is easier to list the states that do have a provision for free ID than to list the ones that do not.
It is also not that simple, it is not just about cost, there are other barriers to getting identification. Availability of DMV offices, limited hours, etc.
Perhaps we should make passport cards free, and then fund an organization to proactively identify and issue cards to every US citizen who does not already have one. Then we can require that card in order to vote.
Problem, of course, is that the US Constitution makes voting a state problem. So we are probably doomed to continue having some states adding as much friction as possible while others seek to eliminate that friction altogether.
For you, it probably isn't. But it isn't like the US makes sure everyone can easily get an ID even if rules state you should be able to get one for free.
The same folks may or may not need to provide more than that to get a Covid vaccine. If they need more, they probably won't get a vaccine. Less, and they will.