She doesn't show empathy for her enemies. But they've always been people who have in her mind hurt/wronged others. She gave the Tarly's, who were not only enemies but arguably traitors as well, a chance to accept her rule. And when two of them still opposed her, she showed no remorse for her enemies.
And while she does want to be seen as a savior, the absence of that, or even losing more friends, doesn't change the fact that she never targeted completely innocent people before. And on the note of being loved, the seven kingdoms would love her once Jon and everyone sung her praises of how she saved them from the Whitewalkers. They could have spread that message across the world after they removed Cercei.
The bold is the important bit. She no longer has advisors to reign her in or give reliable counsel. She's seeing enemies everywhere and is surrounded by people that she see's as betraying her. Look at the way she treats Jon. In her eyes she see's Jon as betraying her because he told his sisters the truth, even though he was completely honest about it to her and never suggested he would lie to them. She no longer trusts him. Tyrion has been so completely off his game since leaving Westeros she has suspicions about his motives (not to mention confiding in Varys before her). Her other remaining advisor tried to poison her and she was forced to kill him. All she has left that she actually trusts are her weapons of war; the unsullied, the dothraki and Drogon.
In her mind, in that moment of isolation, paranoia and pure rage sitting upon Drogon, the people of Kings Landing are no longer innocent. They're her enemies and all she has left is fire and blood. It really isn't that big a jump given she's sitting on the most powerful weapon in Westeros and how rapidly she can dehumanise people in her mind.
And that last half of the last paragraph is ridiculous. Jon couldn't even convince the Northerners even though she fought beside them. The people of the South wouldn't even believe half of the stuff that happened with the Night King. And the promise of love from the people in the future (as unconvincing as that argument is) doesn't help her isolation in the present.