(Spoiler Published), Dany’s War: Is Her Conquest Pointless?

Isn’t the premise of Daenerys waging war to conquer Westeros kind of pointless?

Originally, Daenerys didn’t want to have anything to do with Westeros, that was Viserys's obsession. All Dany wanted was to go back to the house with the red door.

Of course, Viserys's death made her the heir and her marriage to Drogo helped her mature as a person. Also, wielding the ultimate weapon, dragons, would make anyone's mouth water with ideas of conquest.

But if the prophecy of Mirri Maz Duur is true (which, rarely happens in the books) and Daenerys won’t have children, doesn’t that make her whole effort to claim the Iron Throne ultimately futile?

I guess that after crossing continents, waging war that will kill thousands and consolidating power, she could theoretically adopt a successor, like the Roman emperors did. However, Westerosi politics is obsessed with bloodlines and divine legitimacy.

Houses rule because of the strength of their bloodline, and the Faith supports rulers they believe are “worthy.” But if Daenerys has no children, she’d have to either pick a distant relative with Targaryen blood or elect someone she deems worthy.

So what happens after her? Look at Joefrey, a perfectly healthy boy (physically), that Robert never hinted as not being his own, still had his uncles challenging him with powerful houses like the Tyrells backing them.

She could hold a Great Council, but won’t the kingdom go to the highest bidder? And if she perishes suddenly, with no blood heir, wouldn’t her entire conquest unravel the moment she’s gone?