Meh, I feel that most of these issues can be resolved by giving opposing armies siege equipment.
Frankly, the idea of waiting out a siege, as a player, is dull. There is no way that would be an enjoyable experience.
Actively fighting off enemies that can breach your defenses, however, would be interesting.
Actively fighting off enemies that can breach your defenses arbitrarily, such as through digging, not interesting. Honestly, random hostile civs busting into my dining hall without warning would completely kill my desire to play the game. Perhaps the ability to dig through soil-layers, but honestly, the amount of effort it may take to code an AI that could implement that strategy might be prohibitive.
The whole 'self-sufficiency' aspect of dwarven fortresses is a little cheese-ball, but then again, this is sort of supposed to be what makes the dwarves special. Dwarves make the best fortresses, fortresses that are supernaturally good. Goblins don't have to eat, Elves live forever, and Dwarves can create a self-sustaining settlement in an incredibly cramped subterranean space. It's their thing.
As far as the unique nature of the caverns goes... I think that it should be less about a mirror image of the above-ground world, and more about work-able alternatives that accomplish the same end. Like you -should- be able to have grazing beasts in the caverns... But maybe not cows. Maybe giant worms, or something. And perhaps there is a harvest-able moss that you burn or treat to make lye, etc. A player shouldn't be limited by a choice to rely solely on the caverns, in short.