Been a long time since I've watched GoT and I'm not a book person so can't really comment on that.
But I remember there were 2 places where they let her stay for a bit and I like to remember they showed that the places didn't get better, mostly. It just shifted things around. One is the golden mask place. They even bring this point up if I remember. Of course it was one of the previous nobles who brought it up that what they did was bad, but they had order and now it was a place in disorder. Hinting at her being a bad leader overall.
The other place is when Tyrion were the one who brought up the doubt. That place (sorry I'm really bad at names and been a long time) I think showed how she handles dispute among the citizens and it was often in a very childlike 50/50 way.
I remember there were signs of her failings, which is why it surprised me when people acted shocked when she "suddenly" became a tyrant in season 8. I'm sure there are more of it in the books you mention, but to me I think the show did a good job of showing it if you just took a step back and looked at the morals of her actions rather than the morals of her goals.
You are correct with the Rhaenyra. I think people are using it from our outside perspective. Kinda like how people see Halbrand as the Aragorn stand-in even though in actual continuity it doesn't work.
Seeing almost anyone as a hero in a GoT setting (from what I know from the show) is probably not a good idea lol.
I'm mostly watching and thinking "when will this character 'fall'" or "How will they fall".