A war that would psychologically mark later generations, who would insist on still maintaining a North/South Korea DMZ like wall in space.
But the thing is, only the Stileses are "marked". The others barely remember who the Romulans are - and there isn't a single specific reference to how costly or widespread that old war might have been. It takes Stiles and Spock combined to drive home the concept that the Romulans might not calm down if their attack was left unavenged; only these two seem to know how Romulans act in war, and even then, Spock is explicitly only speculating.
And the real enemies of the UFP supposedly aren't stopped by chains of outposts: Klingons roam freely. That Romulans don't is more a sign of current weakness than of past infamy - and that the UFP would build the outpost chain in the first place is a sign of similar weakness in the past as well.
Would any soldier today need a refresher course in history like that before his troopship or plane hit Incheon and his unit moved to the Korean DMZ? The assignment would be (almost) unique but also famous, whereas the Romulan NZ doesn't appear to be the latter.
On the other hand, I could see an introductory speech being given to the troops regardless of need; Kirk could have been prepared to do the standard indoctrination speech before starting his patrol assignment, and now had Spock give a truncated version en route to an active crisis anyway.