Economic warfare does not seem to be "profitable" to me until at least mid game (100 turns in) because the AI usually is not developed enough for it to hurt and it takes a lot of time to recruit, train, and destroy. It seems to work marvelously well against the Mongols once they have settled. You can drag them down quickly to no longer being the richest faction by destroying their buildings especially stables and archery ranges which they will keep on rebuilding.