Sorry if anyone has already said this, but a stronger capital would make small empires slighly more viable compared to large ones, so maybe make the game more enjoable even for those who are not top-ranked. Besides, it makes some sense. In Civ IV the "capital" advantage worked very well I must say. But I am moderately against a standardized start though. At the very least, make it optional, a sort of flaggable option at the beginning. Something that reminds me of the "advanced start" option in Civ IV, where everyone is awarded a certain amount of points, and you can buy everything. In this case, you could buy tile yields for example, research, and whatnot.
Just my 2 cents
I dont mind low-amount of city empires, all the way down to single city empires, and want to say, before I get further, that you should consider there probably will be made a Mod(e), alternate user created addon to the game, that will create advanced benefits for the capital, or to the only player that currently have cities (Think I saw some of the current modders talk about it anyways)
THAT being said, I do not think the approach to single-city viability is to "Artificially Inflate" the power of your capital, but instead give you a decent amount of buildings, in which there can only be one off in an empire, some such or similar benefits would help low-city count factions out, It does not seem to me that the single-city approach is one favoured by the devs at the moment, I played BETA 4 for a few hours today and it seems to favour having at least a couple of cities.
THAT said, you cannot create a game that appeals to every single gamer out there, so you must choose what design goals you really want, and stick with them.
Hope you get the solution you want in the end though, be it capital boosting, or just a mechanic to help the first few cities besides "just a boost", I do want to see you happy 
Sincerely
~ Kongdej