Because in the US the people in charge of issuing suitable state ID have no interest in making it cheap and easy for all eligible voters to obtain such ID.
In fact, in many cases at around the same time they institute voter ID requirements they also reduce the number of places one can go to get ID, with most of the reductions coming to places that mostly serve minority populations.
The supporting documents, such as getting a copy of your birth certificate, often cost money. It often requires significant travel to get to an office that can issue the ID. When the office is in a different city or county, there is often poor public transportation to it making it even harder on those who do not have cars. The offices that can issue ID often are only open on weekdays and only during business hours, meaning many people have to take unpaid time off from work to go.
One can easily blow a whole day on this, or more if there is a long wait at the ID office, assuming that they even can get time off work for it.
A "free" ID ends up costing many people somewhere in the $75-175 range due to document fees, transportation costs, and waiting time.
And if the person was born overseas, this can be a prohibitive cost even for a middle class person.
If you don’t have documents you have no business voting.