I think lone city gaming would be a miss on Stardock's part....and creating the 'capital' would most certainly push towards that end of the spectrum.
I like the way how FE now (as soon as beta 4 is released) requires at least 3 cities to be built to maximize your empire's potential.
I don't think adding a 4th 'captial' type would do anything for the game.
As UmbralAngel brielfly touched on, I would sooner see faction-specific special buildings be made available only to your capital. Things that aren't necessarily overly-abusive....but rather just enough to make your capital the most important city in your empire.
A few non-specific buildings could also be available to your capital, like your castle, warcouncil etc.