Requiring a photo ID for voting is a good way to prevent fraud, that is correct. And many democracies around the world practice it without any problems. But the difference is this: Unlike in the US, in those countries everyone has to have a national photo ID anyway, so requiring voters to show it when voting is no problem. In the US on the other hand, most politicians, often the same ones that now propose this requirement for voting, were against having a nationwide mandatory photo ID.
If they really cared about reducing fraud, they would issue free IDs to every state resident. But if you do it like Perry in Texas, i.e. rushing a bill to require it through the process and then selectively only accept IDs from voter groups likely to support you (e.g. a weapon permit is a valid ID but a college ID is not), it's valid to talk about suppression of certain groups of voters.