That does pose a problem...
Here, you need to present the paper the first time to have your license annotated. After that it is automatic.
Anyway to raise the issue with a government representative like a senator or the governor to have the loophole closed?
I hope you are right and they see the error of their ways and close this loophole. I was shocked at how easy it was for me to obtain the vet status on the license. I wish I could just answer the question for the CDL designation like that... (heh, heh).
About your DD-214, yes I keep my original (now days they have digital copies, unlike when we got them and you had the pink copy given to you), I’ve made numerous photocopies and keep one of them in my wallet. If you ever lose your DD-214, it’s not hard for you (or your spouse/kids) to obtain a copy from vetrecs.com