Why not merge them? Voter IDs can be driver’s licenses, passports, etc. So much bureaucracy. For the sake of efficiency, simply have sign ups for a voter ID card (similar to state IDs) at voting centers. Two birds, one stone. Easy.
I'm with you, it's sadly the nature of the beast. Think about the federal government alone: DoD military ID, veteran's ID, passport, social security card, etc. are all separate organizations with different scopes. It's madness.
So what’s one more, for voting? Or better yet, allow a way to quickly issue people state ID cards at DMV voting centers and other similar facilities. That way you get an ID for voting, and for other state identification purposes. Easy-peasy.
Texas does just that! When you apply for a driver's license or other state ID, you can elect to register to vote at the same time. Two birds, one stone.
Texas is hardly unique in this, since every state except those which continuously since 1994 have either not required registration or offered election day registration is required to do this under the federal National Voter Registration Act of 1993 (the “motor voter” law.)