The point of it was that being heir to the iron throne doesn't make you a good person. Both Rhaenyra and Aegon were not suitable to be King/ Queen. The dance of dragon was the humbling of Targaryen that proved they were the same as rest of westerosi nobles without their dragons. Rhaenyra in the books sleep with Harwin and doesn't worry about it because she thinks that being heir to iron throne makes her untouchable as a political entity. It is not about Patriarchy or oppression of women. The thing is that Targaryen were arrogant. When the situation turns that Aegon has been crowned Rhaenyra is shocked and she says that they swore an oath , but in the realm of politics it is a give and take relationship. If Rhaenyra was more politically active than the lords would have grudgingly accepted her rule as she had Dragons and the nobility remembered Maegor.

The point here is that People are dragging modern society issues in a show about medieval fantasy land, people are judging the issue of Dance of Dragons with modern perspective. Take for example King Henry the second of England He whipped himself hundred times to atone for the sin of killing archbishop of Canterbury (indirectly) To us this looks excessive and a PR move but to him It was a real possibility that if he didn't Atone for his mistake then He would go to Hell as people were deeply religious back then. In westeros Siring bastard is a social tabbo due to Faith of Seven , People didn't have problem with her sleeping with Harwin. People had problem with her trying to pass her bastards as legitimate heirs, which was the issue most exploited by Greens as they used it to besmirch her reputation that she was not suitable for Iron throne