The cost isn't the only issue though. You still have to somehow get to the DMV to get it and oops many Texas DMVs were closed in poorer Democrat leaning areas so it's now a time consuming and expensive journey to go get it. Might be an hour or two away but you can't miss your minimum wage job during business hours or no rent money so what are you going to do? Or say you're old and impoverished and don't have your birth certificate now its a huge problem to get that id. Might be you have to travel to another state and go through a DMV like process to get a copy first and again you don't have the means or time.
Texas' strict voter ID requirement was struck down in the courts last summer precisely because of these reasons. It was found that the law, despite free IDs significantly disadvantages black and latino voter's in the state who are much more likely to have issues like above. Didn't stop polling place workers in some areas though some of whom still turned people away based on the non-existent requirement.