I've talked about Klaus and Rebekah several times, but I don't think I've ever really talked about Klaus and Freya. I've talked about Klaus' abuse to Rebekah, his lack of respect for Rebekah, and how Klaus has issues with women, which are all relevant here.
People like to paint Klaus as being a protective brother, but in reality he is possessive, not protective. He isn't protective over his sisters because he loves them, he is possessive because he doesn't want to be alone.
I'm not saying he doesn't love them, he does in his own way. But he's actually incredibly abusive to both of them. I think it's fascinating how the fandom holds Klaus and either sister up as these "close bonds" when in reality they are so forced by the writers.
Klaus and Rebekah at least have their childhood to explain Rebekah's devotion to her brother. Just like Elijah, she has a twisted need to defend Klaus through everything. In TVD, she did it even more than Elijah. Klaus abused her over and over again and she continued to defend him. A lot of this can be a symptom of abuse. He made her feel so lonely and afraid that if she left him, she would have no one. He made sure she had no one by continuously robbing her of any relationship outside of him. Anytime she would fall in love, he would kill them.
To me, I don't find their relationship sweet because even when they are having their "sweet" moments, it just reminds me of how abusers will apologize and promise to be better. But Klaus never really does better by Rebekah. They just stop being in each others lives. Klaus exiles Rebekah because of the one time she actually tried to defend herself. Then he only calls her back when he needs her to take care of Hope. Once again, we only see them interact when Klaus needs Rebekah to offer herself up to Esther. He compels Marcel to kill her witch body, forcing her back into her vampire body. Then they have brief sweet moments when Rebekah is in and out of their lives until he dies. He doesn't even contact her when he is on a bender for years.
At the very end he "gets" her the cure, although it is not his to offer or promise. Rebekah had the same ability to get it from Elena and Damon. It was just a way to "fix" their relationship without putting in any effort. He never really feels remorse for putting her through hell for a thousand years. Rebekah stated she never got a chance to live and it is because of Klaus.
I get that Claire was out of the show for most of TO which prevented them from repairing their relationships, but given how little effort the writers put into Klaus' familial relationships, I don't think it would have made a difference.
Klaus didn't trust Freya in the beginning and I don't fully blame him for it. But his abuse to her didn't just end with him killing her and tormenting her over her dead unborn child. For most of their relationship, he only spoke to her when he needed a witch or a babysitter. The shift in their relationship comes out of nowhere and is essentially just Freya moving on from the abuse and Klaus continuing to undermine her without apologizing for anything.
They, like with Rebekah, have moments of tenderness from Klaus, but they are few and far between. For the most part, they either don't interact, or when they do Klaus is usually demanding and rude. Freya at least stands up to him more, but it does little to change Klaus' attitude.
I also feel like Klaus just uses the same line with all of his siblings. You have the "You are my sister" moment with Freya which mirrors the "You are a Mikaelson" moment with Kol. He is essentially dismissing their complaints about his abuse because they are family and he loves them. He's all words but no follow through. He promises that family means everything to him but has a thousand years of evidence to say the opposite. I wish Freya had remained more like season 2 Freya with Klaus. The Mikaelsons desperately needed an older sibling to actually protect them against Klaus. Freya would be perfect for this since their relationship started off so bad and she didn't have history with him. Freya initially was, but the writers couldn't let anyone stay mad at Klaus for too long, lest they actually have to hold him accountable for things.
My problem with Klaus and his family or really any relationship, we are told to like their bond more than shown why we should. The only person we see him spend extended amount of time with is Cami. Everyone else he just seems to use and they love him for some reason. But we don't really see him treat them well or earn that love. He just gets unconditional love from his family, which is ironic considering how much he complains about not having that.
Freya naming her son after Klaus was so much fanservice. She clearly would have named her son Finn, you know the brother she had missed for a thousand years and that died protecting her. Even Klaus helping Elijah walk Freya down the aisle was just because the writers had to center Klaus in everything. But he was not the logical choice for that. Throughout the show, we see Elijah and Freya bonding over the hardships of family in a way we don't see with Klaus and Freya.
All of this to say, the writers really failed to develop Klaus' relationships with nearly every character in the show. They used his abusive behavior toward his sisters as the punchline of the joke half of the time. But because the writers throw in a couple of sweet lines, the fandom pretends that Klaus and his sisters were actually close.
Klaus had the ability to be close with his sister and probably had a lot in common with each of them. The writers just cared more about ratings and drama than to center a show about family around the actual family.
Thanks for the ask! Sorry, I kind of went on a rant.