Well, having tried out the Byzantines and Maya so far, I haven't found myself lacking for faith points. This is on emperor, granted. In both bases I had my religion and enhancement set up before I got theology, all my cities converted, and various minors besides. HS in these circumstances is just getting in the way of building something else.
Both games had early starts with faith producing natural wonders. My second city in each game grabbed that and it was an enormous boost. Is this a starting bias for those civs? Or just dumb luck?
I am however going straight for the leaning tower.