No, it's not. Many people have difficulty finding the documents that will get them an ID. There are plenty of people working illegal jobs who are trying to figure out how to get a birth certificate, social security card or prove residence. This was even more common when more people were born at home.
I had a hard time getting ID when I was a teenager, and I needed it for migrant agricultural labor (to work on a legal crew doing corn detasseling.) Luckily, I got arrested a week before we were scheduled to leave, and I was able to con the DMV into issuing an ID based on my jail papers (although the clerk at the jail wrote down whatever I told them.)
The reason requiring ID is a problem is because there's no widespread voter fraud, and declaring that you're someone else is very difficult without that person agreeing not to go vote. It's a requirement whose administration cost dwarfs by orders of magnitude any benefit. The intention is to exclude people who have ID problems, not the people who don't believe it's possible that anyone could possibly have ID problems.
Also, just let felons vote. Put voting booths in prisons. If your population is so prisoner-heavy that they make a significant difference in the outcome, your society is broken.
It would be a step in the right direction, but the concept of a universal ID requires everyone (well, except outlaws in hiding) to have it - if it's mandatory, then it becomes legally reasonable to require it for receiving all kinds of services as you can answer "How do I do X if I don't have a valid ID?" with "Step 1: Get the ID renewed/replaced/made" and "How do I do X without ever getting an ID" with "Sorry, that won't be possible, not ever getting an ID is not a valid option", like it is currently the case in many other countries.
In essence, if instead of "just" making it easy to have ID even for poor and disenfranchised people you go out of your way to ensure that it's weird for them to not have ID, then ID requirements won't suppress voters.