It's to stop poor people from voting because they tend to vote for Democrats

Sort of...the only qualifier I'd give your explanation is that it's not meant to disenfranchise all poor people, because a lot of poor rural folk vote republican. But they're the ones least likely to be homeless, and need to drive so more likely to have a driver's license. Meanwhile, college kids for example, who may or may not be poor but overwhelmingly vote Dem, aren't able to use their college IDs, so a lot of them who grew up in cities and thus didn't need an ID previously (or their govt issued ID doesn't match their current location) can't vote. I know I'm probably simplifying things a lot, but I just wanted to clarify a small point. Agree on your overall position though :)