Although there are few climates where it is absolutely *necessary*, anywhere that gets below freezing it is still *worthwhile* to insulate if you feel motivated and have the materials available, because it will make your life and the chickens' life easier.
By keeping the coop slightly warmer, you can have more ventilation (good) and use less feed for the chickens (good), and not have to spend as much time worrying about cold (good). Insulation in a cold climate also lets you make much better use of other strategies for moderating coop temperature, such as solar heating.
Yes, chickens have lived for thousands of years without insulated coops, but not in upstate NY or colder climates
and in any case, just because it CAN be done does not mean there is no additional value to insulating. I can't see any reason for saying most coops "should not be" insulated, although it is certainly true that most coops "do not absolutely need to be".
I am of the camp that believes a vapor barrier is not necessarily a good thing in a coop -- which functions considerably differently from a *house*, in which a vapor barrier is quite valuable. If you already have insulation with an attached vapor barrier I suppose I'd put it towards the inside of the coop, as that is where the warmth and humidity (such as they are) will be, but you should not have all that much of either, and I doubt it really matters that much in a well managed coop.
Good luck, have fun,
Pat
