Dany was always going to be the one to sit the throne at the end
I think the structure and pacing of ASOIAF highly suggests that Daenerys ends the series ruling Westeros.
The biggest clue is that we are already five books into a planned seven book story and Dany still has not crossed the Narrow Sea. That means one of two things is true. Either George plans to rush her conquest unrealistically fast, or her conquest is not actually supposed to be a long grinding war.
I think the answer is obvious. Her conquest will resemble Aegon’s.
By the time Dany finally lands in Westeros, the realm will already be devastated. Civil wars, famine, winter, Euron, collapsing houses, and eventually the Others will leave the Seven Kingdoms shattered. Most lords will not be in a position to resist a dragon queen with three massive dragons.
And I think the dragons HAVE to become massive before the final book really begins. That is why I still believe some form of time skip happens near the end of Winds of Winter.
George originally planned a five year gap for a reason. He realized the dragons, the Stark children, and the political situation all needed more time to develop naturally. Even though he abandoned the formal gap, the problem itself never disappeared.
My guess is that Winds of Winter becomes an extremely dark book. The Wall falls. The Others begin moving south. Huge portions of Westeros are lost. Winter reaches its absolute worst point and the realm basically starts collapsing. Then near the end of the book, there is some kind of jump forward in time, maybe a few years.
That would allow the dragons to become truly enormous and terrifying by the start of A Dream of Spring. And I think that is important because the final book probably takes place at the very beginning of spring itself. Symbolically it makes too much sense. After the darkest winter imaginable, spring finally begins as humanity fights back.
At that point, Dany arriving in Westeros would not feel like another contestant in the game of thrones. She would feel like the only ruler capable of saving what is left of the world.
And that is why I think most of Westeros eventually rallies behind her. Not because everyone suddenly loves Targaryens, but because dragons become humanity’s only real weapon against the Others.
So no, I do not think the series ends with a Stark defeating Daenerys and taking the throne. I think the surviving Stark children end up allied with her by the end. The political conflicts that dominated the early books eventually become secondary to survival itself.
The final war is ice versus fire. And fire wins.