Robert made the point in season one on the dangers of a united army and the overall instability of the realm, as did Jorah on what people want, which is simply to be safe, fed, and happy. A lot of blood will be spilled with Dany rolls over, but she's quite likely to be sympathetic to any who'll kneel, of which will be plenty if she has a gigantic fuck off army, reputation for kindness towards her people, and three dragons ruining shit. You'd have a lot of houses who couldn't give a fuck about who is currently on the throne, maybe even want it themselves, making a correct assumption that fighting her spells doom.
Divide and conquer, and all that. The more fractured the realm is, ironically a fault of their own, the easier she'll steamroll over them.
But given we're four seasons in and she's still wandering fictional Middle East freeing slaves while her dragons grow I suspect her character arc does not involve simply travelling to Westeros and starting a war. My hunch is that her arrival will coincide with a whole heap of other shit going on, like the white walkers.