The basic structure is: build your city, raise an army, sack the surroundings. Sort of like Civ, but with hundreds or thousands of other players. The problem is that the real game is coordinating with other players in an alliance. Whatever skill you might have at managing the growth curve or basic tactics is swamped by the reality that even a small alliance can overwhelm a single player. So you need to find a larger group to be part of. But larger alliances still overwhelm smaller ones, and the skill set necessary to have an enjoyable game is about recruiting and coordinating. Most members of the alliance are merely taking orders, and the only meaningful confrontations take place on huge scales.
Some games put limits on this by requiring investment of resources to grow alliances larger. This only bends the curve; it doesn't change what the game is really about.
In contrast, a game like Puzzle Pirates or even EVE has both single-player and group actions be meaningful. You don't have to join a crew or a corporation in order to play the game. Sure, you'll miss out on some of the features and scope, but you can still tell your own story and have your own goals. Same with WoW--- you can't do the biggest dungeons without a group, but neither are you required to join a guild to get anywhere.
Other growth games limit who you may battle to those close in strength to your own. This feels closer to the correct design to make me happy, but seems very artificial in practice. You lose a sense of "space" for your kingdom (or whatever).
So maybe what I want just isn't possible. I'd like a growth + combat game, but not one that requires you to join a massive side to survive.