At a minimum it provides more confidence and faith in the voting system. That’s not a small benefit.
It also provides a safeguard against fraud in future elections.
It’s easily worth the small cost of requiring an ID.
The real reason the Democrats strongly oppose it is they currently have a lock on the “don’t care about or follow politics but can be dragged along by friends” votes.
I think you may underestimate just how hard it is to obtain ID in most of America. First, you have to locate the 5+ forms: birth certificate, multiple bills in your name at your address, previous id if any, etc. Many people (homeless people come to mind) would never be able to obtain all these records. Trying to obtain a drivers license at age 18 was a massive undertaking and myself and my family and had lived in the exact same house for my entire life!
Now imagine. You're poor. You're working multiple jobs, taking care of your children, etc. Even if you manage to come into the DMV on the first try with all the forms perfectly ready and in order - something the DMV makes nearly impossible - you will still probably going to wait 2+ hours to even get up to the window to start the process. When you add up traveling to the DMV, being there, and coming back, you could be missing the vast majority of a day of work, something that can get many minimum-wage workers fired.
In the abstract, requiring stringent ID to vote seems like something everyone should get behind. In practice in the United States, these laws are only enacted by Republicans that are threatened by shifting demographics. If all poor people in major population centers were voting, the Republican party would all but evaporate, or have to severely alter its message
There's no evidence suggesting a meaningful amount of false votes are being cast by people without IDs. So if you don't think fraud is going on, you won't be more confident. If you do think fraud is happening without any substantial evidence, why would this change make you more confident?
Additionally, allowing voting without an ID also provides confidence and faith in the voting system. Why trust a voting system that rejects people for forgetting their wallet or for being a walking teetotaler?
It adds cost and there is no indication of an actual existing problem that it would solve that justifies the cost. Even if you ignore the fact that all actual voter ID proposals have been fairly overtly aimed at discouraging voting among selected groups of eligible voters that tend to vote in a way unfavorable to the preferences of those promoting voter ID, or that several times implementation of voter ID has been accompanied by targeted efforts to reduce access to new/replacement IDs in areas where, again, disfavored voters by the group advancing voter ID love, and even the more basic fact that it adds another point of potential failure due to human error even when pursued honestly, the fact that it to all indications provides nothing of value for the direct, immediate added cost is enough reason to oppose it.