Dan, the answer is you are probably too young. Look at those WW2 veterans, many just chucked their medals in a drawer or let the kids play with them. Now, with the war reduced to TV and Hollywood they are the remaining living history. Even now many don't remember the Cold War and for many civilians the terror. Maybe not constant fear but fearful never the less.
Another more subtle use for veterans ID as in the discount cards is advertising. The more people showing these cards will advertise the presence of quite ordinary people in the community.
Quite when a simple Veterans ID would be useful however is questionable. What happened to the PM's great idea of displaying it on your driving licence? I also remember when you did NOT show Armed Forces in your passport. I imagine there are places where you do not want to show an ID.