Your argument is all over the place and just biased in favor in Rhae anyone who already supported Aegon wouldn't see it as moral failing, but as a necessary response. In fact they would probably be pissed if he didn't respond equally see World War 2 with the escalation of bombing campaigns. Second off the fact that she burned down a major center of the Faith would piss people off especially since her major backers are the North whom even after close to 3 centuries of United rule are considered as fairly heathen. Much less much earlier in the timeline.
Anyway Rhaenarys can justify her actions and spin it. Aegon can do the same for his actions and use the fact that she struck with such an utter escalation of force as a rallying cry, "Remember Oldtown". Burning down an entire city as her first action would cause all sympathy for her to dry up. I'm not saying it would necessarily or even likely cause her loyalist to defect or even just decide to sit out the war. Many would likely still fully support her. But as we have seen in real life unrestricted bombing campaigns rarely break someone's will to fight in fact often the cause them to rally and fight harder, and unlike with the conquest the other side isn't totally helpless to dragons outside of some theoretical golden bullet moment.
It's not a matter of spin, at least not really. It is a matter of capability.
Aegon has to keep a combat capable dragon in King's Landing. He has three; his, his wife's, and his brothers.
He has to keep a dragon with any substantial army that he fields.
That leaves one theoretical dragon to either conduct offensive operations or to defend another location.
Rhae on the other hand? She doesn't really have any cities or vulnerable bases of operation. Aegon can't torch Dragonstone. If he goes and burns the North then he gets a full blown religious war as the First Men go to town.
Then you have the question of what both sides need/want. Rhae just need the nobles to sit in their castles and do nothing. She already has the naval power, she already has the dragons, she already has an army, and she already has gold.
Aegon, on the other hand, needs those nobles to actively support him. His primary support base was just destroyed. No one has really actually declared for him yet, especially any of the great nobles.
In terms of legitimacy, Rhae is 1) the named heir, 2) the one who all of the nobles swore fealty to as the heir, and 3) the eldest child. Aegon didn't try and summon a Grand Council to name himself king, he just declared that he was king and basically expected High Tower support to keep his ass on the throne.
In this situation, the High Towers are gone. The leadership of the Faith is gone. The leadership of the Maesters is gone. And EVERY noble in the Seven Kingdoms has to way supporting him against the threat of a dragon coming along and burning their holdings to ash.
Rhae can make the, legitimate, argument that she is just punishing oath breaking. Her threat is "break the oath you swore and I burn your castle. Do nothing and I leave you alone.". Aegon's threat is "Kneel to me, give me your men so I can usurp my sister. Or I burn your castle."
In those circumstances, who exactly do you expect to openly support Aegon? None of the Lords Paramount are going to lift a finger to support him until they see someone else test the waters. And the first lesser noble to do so will get his castle torched. Who is willing to test Rhae after that?
If Rhae wants to win, she has to immediately go all in and prove that she is willing to go all the way. She needs to act before the nobles declare for Aegon, because once they have publicly supported him it is a lot harder to get things to go her way.
But by moving before they publicly declare, she gets the frame the issue how she wants.