This is a good way of reasoning.
Is neutrality a kind of cosmic chaos in nature?
There should be capture conditions for those buildings.
That religious buildings contribute "morality" or "loyalty"
The Houses too, the family that lives in the houses, and the gods are also part of the land.
yep, the fact that map size and playable area so strongly affects cavalry balance is good evidence that their speed is too great a share of their balancing.
I think it would be good to bring them closer to infantry units and differentiate their roles (as opposed to just being faster, better infantry for the most part). This is made much more difficult by the fact that CS infantry are economic assets while CS cavalry are not, but improvements are still possible.