There's a small chance of Gendry even getting near the Iron Throne.

Brienne, Arya, Jon Snow, Tyrion, Theon, Sansa and Varys.

Brienne - Brienne only wants to serve, she isn't interested in ruling at all... And I feel like she wouldn't really be well suited for it either... She is a great fighter but she doesn't seem to have the ruling qualities.

Arya - This girl is in a mess half across the world? She is about to become no one, which means forgetting about all these things, AND she is too far away AND she is too well known to come near Kings Landing AND she doesn't have anything to take Kings Landing with.

Jon Snow - I believe it has been confirmed that he will return but even when that is true... How does he return? Zombie? Or weak and injured like Berik? I think people who believe he will take the throne is just a dream thing! It would be cool and all... But it's not realistic at all, especially not anymore, and he have decided to give everything to the night watch! Nothing else really matters to him anymore.

Tyrion - He is pretty much one of the most hated people in Kings Landing now... How could he possibly rule it? He does have the qualities but no one can rule without the people.

Theon - Or should we call him Reek? Because that is pretty much all he is... He have become a nobody and there is no way he can get the throne... He has nothing, he doesn't have the ruling qualities and he can barely speak.

Sansa - This one is interesting, because a lot of people seem to think that she will definitely rule, but I wonder why? Because she improved and got better at the game? Well sorry for saying this but you will need A LOT more than that! Sansa doesn't have anything either, no army or anything to support her, and you can't really take a city by being a lovable character and because you got better at playing. Sansa ruling is definitely also a dream thing... It will never happen, unless she gets to a castle who wants to fight for her, then there is little hope. However she does have the ruling qualities I think.

Varys - He has NO interest in ruling at all. But that's really it, maybe he wouldn't be that bad at it.

A lot of these, but her entire story arc is showing why she'd be the worst possible ruler and deconstructing her whole "savior" tropes. In fact, I think it's likely that she'll prove to be a bigger threat to Westeros once rejected than the white walkers