I got lucky, kind of. When I was Active Duty, I lost my ID, had another one printed. Then I found my first ID (you know, the one they take when you are in Basic and have no hair). So now I have two legit ones. So when I separated, I turned in the older one and kept the newer one. Granted, it's been expired for like 9+ years now, but I still use it to get out of traffic tickets and now, free food.
But you are correct; if you are a Veteran that did not retire or are active duty, you really shouldn't even have an ID.