I do hear alot of negative comments about the N.A.s, but, it all depends on how they are used.
I just had an Emperor game, playing Roosevelt.
Sitting Bull declared war on me, 2 tiles away from my horse resourse. He pillaged it and sat on it with a chariot, a dog soldier, and a shock, combat 1, drill 1, CG1 archer.
Then came his reinforcements of more of the same.
As my copper was in the radius 2 of my 2nd city, and I hadn't cultured out to it yet, I was forced to build more archers to defend my city.
These kinds of pillaging raids can be devastating to empires (like Rome) that heavily rely on a resourse to become powerful.
Eventually, I cultured in the copper and parked 3 combat 1 archers on it, until I could build axemen and spearmen. His stack of 7 units attacked my walled hilled city and he lost, but, he had twice as many cities as I did, and was clearly in a better position, than I was, at the time.