And despite Jon's own (increasingly) royal status, it now seems extremely unlikely that Dany will rule Westeros when you consider not only the theft of her army and plotline but the ham-fisted assassination of her character in the last episode.
[eye roll]
In an unbearable face-off between Dany and Tyrion, she trash talks "heroes" for doing the "stupidest, bravest" things—the exact kind of deeds she committed a mere two episodes ago when she ignored her advisors and charged into battle to burn the Lannister army, or when she confronted the warlocks of Qarth, to name a few examples.
She was frustrated that Jon, whom she was just beginning to reconcile her own feeling for, had gone off on a foolhardy mission that may kill him and was lashing out. She was trashing part of what made her love him which was likely part of a defense mechanism to cushion the blow of his possible loss.
Then, she refuses to admit that she's ever lost her temper—something that we've seen her proudly defend in season two, when she puffs out her chest after Xaro Xhoan Daxos says, "She is the Mother of Dragons, do you expect her to watch her people starve without breathing fire?"
She knew Tyrion wasn't talking about that, she knew he was referring to her treatment of the Tarlys, and she didn't agree that was an instance of her temper; she believes she acted properly.
And perhaps worst of all, Dany dismisses all of Tyrion's questions about her plans to "break the wheel," repeatedly telling him, "We will discuss the succession after I wear the crown." This felt like the deepest betrayal of her character, and it seems utterly implausible that the topic of what to do after conquering a continent with a horde of bloodriders has never come up.
She likes Tyrion, she respects Tyrion, and she trusts Tyrion, but she's still annoyed that his plans and lack of foresight lost her allies and somewhere in the back of her mind (and she even said it aloud) she wonders if Tyrion is pulling his punches in an attempt to not inflict too much suffering upon Lannister forces and their (his former) compatriots. And she's probably right; Tyrions plans likely reflect that bias, but since he won't admit to this perhaps Daenarys wonders if he doesn't have another more selfish reason for wanting to leave the old power-structure intact; perhaps because he would fit nicely into it. (I don't think that, but from Danys' perspective...)
Why would Dany, who successfully fought battles for a more egalitarian society in Slavers' Bay with the help of advisors both foreign and native to the region, refuse to discuss how to destroy Westeros's current ruling class with one of the most powerful Westerosi leaders from a respected house?
That's not what that conversation was about, it was about what came after.
This just comes down to: "Waaaa, waaaa, they're doing stuff I don't like with my favorite character, waaaa, waaaa!"