Invade a country strike the hospital first... because that is were all their able soldiers, storage resources, and military deployment are... i am not saying that disabling the medical buildings of a country is a bad idea but there are plenty of places more important to attack before going thinking to secure the hospitals (which as an invading force should be secured for yourself, after all a hospital can come quite handy, even more if your own troops suffer damage and then you have to take care of them, this way you can attend to them in place), however quite some time will happen before you get to start securing the hospital, places like military stations, the town hall, and other lines of defense and political influence inside the town take priority.

If the war drags on and it becomes a battle of attrition you need to limit the intake of resources and reserves of the enemy, in that case we start seeing places like the hospital as principal targets.

TL:DR they still had time to go to the hospital, and then leave the town.

Plot building...not bad, not bad....