I feel like you're forgetting she's got Dorne and Tyrell forces now too.
That's why I said, "the possibility of being granted a kingdom outright to use as a foothold", though Dorne is probably the worst one to have for those purposes. (Okay, the Iron Isles would be the worst, but Dorne's a close second. Proximity and crop yield are ridiculously important factors for medieval warfare.)
Not to mention you shouldn't discount the dragons when it comes to a siege situation. We saw how easy it was for a single giant to prevent a siege at Winterfell, now imagine three dragons just straight up flying over the courtyard and literally melting the stone walls around the gate of a castle, blasting fire at any building turning it into an oven and roasting those inside.
... and that would be why I said "Deus Ex Draco". I fully expect them to treat the dragons as a narrative solution to anything and everything.
Though, again, realistically: there are three of them, and they aren't immortal. If she splits them up, the chances of losing them increases dramatically, and one dragon per castle doesn't put her very deep into Westeros before she stalls out. If she keeps them together, she can only roll over one castle at a time; she's basically got a roving rape-gang, not an actual conquering army. If she burns castles to the ground, she's got no way to hold onto the lands she's taken short of leaving massive numbers of troops behind to occupy them.
Taking over a large amount of territory and actually holding it with infantry is incredibly difficult; Daenerys couldn't even successfully hold more than one city in Slaver's Bay at a time, for reference. As should surprise no one, at some point it's going to come down to politics whether or not she can
actually conquer Westeros as opposed to just wrecking everyone's shit and then getting bored and going home.