Your confusion is probably because the problem is not as straight-forward as it seems.
(1) "Requiring an ID" - This was never about requiring an ID. This is about requiring a very narrow group of photographic IDs, only. Need a government issued photo ID? What if you don't have one, but have all the documentation needed to obtain one? Not good enough. So that's good enough to get the photo ID, but not to substitute as one.
In many municipalities you used be allowed to supply a lesser form of photographic ID, along with other documentation, in combination. That's not accepted under these laws.
(2) Which IDs are OK? Driver's licence is fine. Passport is fine. Not everyone can easily get these, or there is a cost associated with them.
College student IDs (tend to be more liberal in voting habits) - no good in many states. Gun permit? Good. A VA card, used to collect federal veteran benefits? Not accepted under many of the laws. Clearly, it's not just about having "a form of ID" or even "a form of photo ID."
(3) Everyone should have one, right? Claims that you have to have one to collect benefits or open a financial account are meaningless. I can open financial accounts online, without supplying a photo ID. Many of the elderly may have had some of the IDs at one time, but no longer do (no longer drive, for instance), and established their benefits and financial accounts decades ago, and have been voting non-stop ever since. Many of the elderly also no longer can get out and about like they used to be able to. Others, like members of religious orders, do not have those kinds of accounts, or drive, but, as citizens, should be able to vote.
(4) It's easy to get, right? There are many groups of people who can't easily get a government issued ID. Access to locations, especially in more rural areas, the need to have transportation to get to them, the ability of hourly minimum-wage workers to take time off when they don't have scheduling flexibility or paid time off, etc etc etc. It doesn't matter if you deem it a minor inconvenience, or if it's a brick wall. ANY requirement that creates a burden that falls specifically on a particular group or groups is going to have a skewed impact on elections.
When Mississippi first instituted their voter ID requirements, you needed a birth certificate to get a valid, accepted photo ID. If you didn't have a birth certificate? No problem..... if you have the photo ID required to get one. Oops.
Many poor, older, rural citizens were not born in hospitals and were never issued a birth certificate. There was another case of a man in Wisconsin where there was a clerical error on his certificate (born in another state), so he could not get a photo ID, and the hurdles to getting valid documentation were enormously expensive and cumbersome.
Bill Moyers - Black man in Wisconsin brought three forms of ID to the polls and couldn't vote
(5) What's the history in the USA regarding obstacles to voting? In the days of institutionalized racism via Jim Crowe and other laws, there were "poll taxes" or fees to vote, which blocked the poorest from voting, and arbitrarily administered "literacy" or civics tests where a white voter might, say, get asked to recite the Pledge of Allegiance, and a black voter might get asked to name the Massachusetts delegates who signed the US Constitution.
Today, those more likely to not have these forms of voter IDs, or have difficulty getting them come from demographic groups that tend to vote Democratic. Coincidence?
Those kinds of measures were deemed illegal obstacles, meant to prevent people from exercising their rights. If you require someone who was never issued a birth certificate to have one, that is a process that can take months and can cost hundreds of dollars. That's a de-facto poll tax.
(6) It's needed to address voter fraud, right? - No, it's actually not. While there are various kinds of illegal voting, or voter fraud that happens, the kind that would be stopped by a photo ID - in-person voter impersonation of a legitimate voter by someone else happens almost never, at all. Voter fraud, because of it's one-by-one methodology, is almost impossible to tip any election unless there was a massive, coordinated effort of many, many, many people. That is not the case. Now, ELECTION fraud is a real threat, but that is not addressed by voter ID laws. In fact, voter suppression of legitimate voters would be considered election fraud, by most measures.
This is a solution in search of a problem. In lawsuits challenging voter ID laws in many states, and definitely in Pennsylvania and Wisconsin, supporters of those laws admitted, in court, that they could not find a single instance of this kind of fraud.
Ahead of trial, Pennsylvania admits there is no voter fraud problem
So, when you look at the fact that requiring a narrow subset of IDs that CAN BE more difficult for some demographic groups to get vs others, to address a problem that does not exist, what you have is a targeted attempt to make it harder for some groups to vote. It's 100% a voter suppression measure.
The argument that "hey, 99% of people should be able to get an ID" means that you are willingly disenfranchising 1% of the legitimate, legal voting population for something that happens a handful time out of hundreds of million votes cast. It does not make sense, if your goal is integrity.
The Truth About Voter Fraud - Brennan Center study on voter fraud