There are some really good thoughts in this thread, this is taking a good direction!
General thoughts:
- The possibilities given through the order tree seem to help balance wide vs. tall very well. Maybe we should just move some similar bonuses to the liberty tree (or some other earlier tree - exploration maybe? Ahriman once said this has been discussed and dismissed, though...)
- In order to improve wide without making it overpowered, I think we should focus on ways to help new cities catch up quicklier without making them much stronger later on.
- I'm rather bad in maths, but it seems that e.g. one more science per city does exactly what we might desire - it helps an wide strategy early on, but loses relevance later on, both when the city grows and when we already have many cities. Or am I wrong?
- While not every yield should be available in a completely undevoloped city without any policies (culture!), the more yield per city we have, the less we're dependent on yields from a palace (or multiple palaces). I have seen some very convincing arguments that the problem of building everything in the capital is small already in CEP, so small adjustmets might eliminate it completely.
Let's do some number-crunching:
Currently each city gets 3

4

1

, + 1

when founded on a mountain (which is weird IMO and should be cut if possible). The 3 palaces each give 2

2

2

2

2

.
I'd suggest 1

1

extra per city, plus an adaptation of the internal trade formula (so roads are more profitable and wide empire get a bit more money).
For the single palace in the capital I'd only suggest 1

1

or something along these lines.
I'm not sure about culture. Not having the 3x2

from the palaces seems like a lot, but then again we only have 1 single culture on the palace in vanilla BNW, and that's the only culture we get before monuments or tradition/liberty openers. How much can we adapt the policy cost formula to not be dependent too much on the "free" culture now given in CEP through the 3 palaces?
On the other hand, is there even a downside to having free culture on the palace? We don't have a national wonder any more that boosts culture, and tourism is the main factor for a culture victory...
And, sorry, but I'm too tired to make up my mind about happiness and where it should come from
Just one final question: Which yields can we make national already now without much effort?