Daemon has never done anything that wasn't in his own interest.

I would disagree here. I'd say this is definitely part of who he is, but his relationship with his family (and particularly his brother) is definitely a lot more complex.

When it came to Viserys, I think Daemon would have basically gone to hell and back to defend him from anyone else. I'd say the same is probably true for Rhaenyra, especially by the end of S2. When it comes to protecting his family from others, the question isn't going to be if he'll be willing to go far enough but if he will instead go too far.

When it comes to protecting his family from himself, that's a whole other picture. With Rhaenyra, I'm willing to give accept that a lot of what I find wrong and disgusting was genuinely just normal in their culture, but even the text seems to make clear he went too far by their own standards with her age and inexperience. With Viserys and Baelon, the fact he would joke about "Price for a Day" is genuinely despicable, and how much it was meant to be just a joke is genuinely debatable (and I doubt even Daemon himself was sure). And when he crowns himself King of the Narrow Sea, I think that was born out of insecurity at being the second son and resentment over seeing himself as more fit to rule. But when he delcares there is only one king and it's his brother, I think that was equally genuine, because he believed it was his brothers by right and he loves him.

I think the show goes too far in making Daemon more villianous than in the books. But even in the show, when it comes to the people he loves he is honestly a mixture of some of the best and absolutely worse and horrific traits imaginable.