Agreed. All that's needed is a 4th type of city state, Religious. Then we'd just need to decide what benefits these city states give and to think of some quests. Anything more complicated than that will end up detracting from the game.
I think of something along these lines:
Characteristics:
* More unncommon than other type of city states (there will be just a few each gameplay session)
* You can only be allied / aligned with one religious city state at the time. Just as it happens on the real life, religions tends to do not bode well with competition. Your empire is either Catholic (friend of the Vatican) or Buddhist (friend of Lhasa), but not both.
* However, they give a Big happiness bonus if you are allied (say, a whooping +10 happiness bonus, equivalent to two different luxury resources)
* ...and add an unhappiness penalty if you piss a religious city state off (say, -5 of empire wide unhappiness). That way you accomplish the following:
- Religious city states will be extremely important to the stability of your empire, just as it happened on real life.
- However, most of the religious city states will be a pain in your ass since you can only ally with one of them at the time, having to satisfy their demands, or else your empire will suffer from religious protests. That way, you will be forced to either devote a good amount of resources to appease them or you know, initiate a holy war in order to recover holy land and prevent your empire's unhappiness, kinda like China's anexation of the Tibet.
- Buuuut since the common thing will be that several empires will be allied with one single religious state due to their rarity, attacking one religious state is basically kicking a hornet nest and even if it will solve your inmediate unhappiness problem, it is probably going to create a major horsehockystorm... just as it happens in real life (think the whole Jerrusalem / Palestine situation).
Also, in order to mitigate the effects of religious city states it would be cool if there would be
social policies devouted to deal with them:
* Freedom of religion. You can befriend more than one city state at the time
* Religious caste. +150% to the happiness generated by religious city states.
Of course, both would be mutually exclusive branches of the piety tree
also, add in for good measure in the scientific tree:
* Atheism. City states do not generate unhappiness in your empire.
And to wrap everything up...
Quests:
Patron Saint: Build X number of monasteries in your cities.
Closer to God: Build a Religion - oriented wonder (Sixtine chapel, Stonhege, etc).
Lord of the choosen people: Make a certain city celebrate the "we love the king's day".
Holy war: Wage war against other religious city state.
Holy land: Claim for your empire a choosen natural wonder, by any means necessary.
Pillgrimage: Transport one of your military units into one unhabited, designated hex (far, far away from your civ, that is).
Holy relic: A nearby goodie hut contains a forgotten holy relic. Transport it back to the city state, spaceship style, in order to obtain it.
Pacifism: Disband a number of your own military units!
Reconciliation: Make peace with one of the civs which you are currently at war with.