The main demographics that has it "the worst" are
Significantly older people, who were born so far ago that the chances of them having lost their main documents (e.g. birth certificate) are higher, the chances that they have recently needed some sort of ID is lower (they haven't traveled in a while) and the chances to reconstitute their identity are lower (it's easy to get a copy of birth certificate from 30 years ago, but probably less likely from 90 years ago for a variety of reasons).
Truly homeless, who have no proof of address (which is usually a hard to avoid step in obtaining other documents). Of course, some shelters offer proof of address, but I doubt many homeless have a shelter spot.
If you discount those two edge cases, no demographic can legitimately claim "difficulty" in obtaining and especially "maintaining" an ID as a mass of people (yes, you can always find anecdotal sob story or two, but as we all know, multiple of "anecdote" isn't "data").
First of all, because majority of states have extremely lax voting "ID" requirements, if you call them that. For example, California, as documented in my answer here citing CA's official documents, requires - at the very worst case (and there are less onerous ways to vote), one of each of the following 2 categories:
(1) Current and valid photo identification provided by a third party in the ordinary course of business that includes the name and photograph of the individual presenting it. Examples of photo identification include, but are not limited to, the following documents
(E) credit or debit card; (G) student identification card; (H) health club identification card; (I) insurance plan identification card; (J) public housing identification card.
Note that even a picture credit card is acceptable - when I used to have one, the maintenance cost was literally $0 - of course, I was one of those conscientious people who paid off my CC bill on time and generally used CC as a debit card, incurring no interest or fees (as a poor recent first generation immigrant, before someone starts screaming some Marxist 'privilege' argument).
And a driver's license or a non-drivers ID typically cost $25 to renew every 4 years (these are NJ costs), so the "maintenance" cost is $6/year even for that. As it can be done by mail, you cannot claim labor/transportation costs, but I suppose it would be fair to add 60 cents on a stamp, for annualized 15 extra cents of cost.
(2) Any of the following documents, provided that the document includes the name and address of the individual presenting it, and is dated since the date of the last general election...
(A) utility bill; (B) bank statement; (C) government check; (O) identification documents issued by governmental disability agencies; (P) identification documents issued by government homeless shelters and other government temporary or transitional facilities.
Again, the "maintenance" cost to having one of these is $0 - everyone has one, including the homeless in shelters. And nearly everyone either pays bills, OR, gets paychecks, OR gets government assistance, which means they have a guaranteed form of acceptable ID for this.
The acceptable IDs even include justice system discharge papers, meaning you can't even claim that people who were imprisoned are somehow negatively affected as a group.
Even if you take the most strict possible law (like Kansas's recently overturned one), the difficulty is minimal.
First time voters only are required to show an ID that proves citizenship, such as Birth certificate; U.S. passport; U.S. naturalization documents.
The cost of birth certificate to a person is $0 (their parents paid it) and it never expires, so $0 "maintenance" cost. Even in the outlier unlikely case that they lost their birth certificate, a copy can be obtained cheaply (an expensive state like NY charges only $17.75). Remember that to even need this cost, you must have BOTH lost your birth certificate AND have never been registered to vote.
The cost of certificate of naturalization is $0. You get it for free when you become a citizen (reference: my own experience). If you're a naturalized citizen, you have that document as a free byproduct of a (otherwise rather expensive) process. And it never expires, so maintenance cost is also $0.
The cost to "maintain" a US passport is as per @njuffa's comment $11/year ($110/10 years) or $13/year for first time passport applicants. They are renewable by mail and therefore also have no transportation/labour cost.
Again, an important point is that, while the question - and much discussion on the topic - starts with an extreme case scenario of "if they did not obtain the id", in reality, an overwhelming majority of US citizens already possess on of the acceptable forms of ID just to be able to live here. You cannot board an airplane, or a train, or drive a car without an ID. You cannot get government assistance without an ID, so that immediately cancels out low-income people who get government assistance from your list of possibly affected people.