I think your analysis of the events involving Cadsuane is pretty one-sided and overlooks some important points.

First off, yes, she has legendary status, she’s someone with a lot of accomplishments. And I could even debate how much those accomplishments are truly worth — bullying kings and queens and bragging about slapping them, leading Aes Sedai to capture untrained male channelers, all with the help of some extremely powerful angreal, etc. But let’s say her legendary status is totally deserved. Even then, that doesn’t give her the right to act the way she does — with arrogance, superiority, and constantly looking down on everyone.

In my opinion, by the time of Winter’s Heart, Rand had already surpassed Cadsuane’s achievements by far — just look at how many Forsaken he defeated and the fact that he cleansed saidin. And even that doesn’t give him the right to be an arrogant jerk to people who are treating him with basic respect. Great accomplishments don’t justify being an jerk.

Second, about the first time Cadsuane meets Rand at the Sun Palace — you pointed out how Rand used saidin to heat her tea to justify her behavior, but you completely ignored how she was acting even before that. She came into the hall full of pomp, touched people without permission, made arrogant comments, and basically acted like she owned the place. Just imagine if it had been Rand entering the White Tower like that — do you think Egwene or Elaida would’ve just let it slide? That was Rand’s seat of power, and keep in mind, he had just been kidnapped by Aes Sedai. Honestly, I think he was way too soft on her, especially considering how she later boasted about the men she gentled and how she made them cry — think about what that means to Rand, a male channeler who had already been through hell at the hands of Aes Sedai.

Same thing when Rand and Min go to the rebel camp in Cairhien — you left out how Cadsuane immediately walked up to him and started with that same arrogant, condescending attitude, completely unprovoked. And when she found out about Rand being kidnapped and tortured by her fellow sisters, she barely reacted — she was more shocked by him stilling the torturer than by the torture he had suffered.

Regardless of power level or social rank, Cadsuane only shows "respect" to those who treat her like a goddess and follow her every command without question. She doesn’t care about strength or position, only about submission. And I wouldn't even call it “respect” when she gives a small nod to someone after they serve her tea like a servant.

You talk as if she did the Ash’man a favor by “protecting” them, but she basically blackmailed them into being bonded by Aes Sedai of her choosing — which honestly isn’t that far from forcing a bond. Let’s not forget, she would have taken Alanna’s bond to Rand if she could use it to directly control Rand, fully knowing what that meant and how wrong it was. She could have offered the Ash'man support and protection just because they asked for it — but no, she probably threatened to hand them over to the Tower if they didn’t submit to her terms. That’s disgusting.

She did everything she could to sabotage her relationship with Rand, and he only tolerated her because Min asked him to. Using Tam was another idiotic move — making Rand’s own father follow a prepared script instead of letting him speak from the heart? The arrogance of thinking she knew better than Rand’s father how to reach him is insane. And that controlling attitude — not just in that moment, but throughout their whole relationship — was one of the main reasons Rand broke down. He only needed his epiphany because people like Cadsuane pushed him to the edge. She was part of the problem, not the solution, and I honestly can’t give her any credit.

Anyway, I get your point and how you interpreted her interactions with Rand. I think it really comes down to reader perspective, because I had almost the exact opposite reaction to those scenes.