Higher Game
National Socialist
Building a shrine is a good idea if you have a prophet (sometimes you will) and a holy city that can output more right away, or have enough potential for spread (auto, or zealous neighbour) to be better than the value of settling him.
Actively foregoing a great merchant/scientist for a prophet intended for a shrine is probably done way too often compared to how often it is a good play.
But to get back to the AW, which triggered the whole discussion. It can happen, and has happened to me a few times that I have captured a holy city of great influence, that just happens to have no shrine. The AW is a great option to quickly push out a prophet for a shrine then. And if the game is not going to end in the near future, then with multipliers, particularly if you are planning a corporate HQ/Wall Street city there, it will easily be one of the most profitable great people you generated that game.
A high commerce, low hammer city needs a prophet specialist far more than a shrine. Those hammers lead to infrastructure, enough that the shrine had better put out 15+ gold a turn to be competitive. I see that mostly with buddhism and hinduism, but those are religions you let the AI take, and warring over them is very situational; Arabia is protective and the Byzantines are usually just too big and scary to take on. Spain, however, is usually a nice target.
Hmm... one wonder that the game was lacking, would have been one which unlocks a free GG. It would have been interesting to have this one available early on in the game, which could still give peace-builders a chance to gain a GG without an early war. It would be interesting to see how much this one would be contested for...
Not much, unless it's really cheap. A GG is worth thousands of hammers later, but so is ignoring early wonders and rushing your neighbor. I do wish the HE gave GG points.