The problem with that in the US is that we have no form of ID that almost anyone who is eligible can obtain for free or very low cost.
We mostly use driver's licenses, and for people who don't drive states also offer IDs that look a lot like driver's licenses but are only for ID and are issued by the same agency that issues driver's licenses.
In many states they have closed many of the licensing offices, and cut back the hours licenses are issued at others. The closures happen disproportionately in poorer areas with a higher percentage of non-drivers. The reduced hours often leave office issuing licenses and IDs on weekdays in the middle of the day.
This can result in having to take a long trip on public transit to reach an office, and a long trip back, taking up much of your day. For many poor working people that can mean a day's wages lost.
The lost wages, transportation costs, and fees for the license or ID can come to over $100 which is a lot for many poorer people.
If we introduced an ID that is given to every citizen when they become old enough to vote, at no cost to them, and that can be obtained easily locally there would be little objection to requiring that to vote.
But most of the politicians pushing for voter ID are the ones that most benefit when poorer people cannot vote, and so tend to also be opposed to making the ID cheap and easy for eligible voters to obtain (and are also the ones closing license offices and reducing hours).