No, I don't think it is a bad idea. It sounds like it's not going to change anything. Maybe including a handwritten note would help. You seem to really dislike your sister. It sounds like she has figured that out. If she believes that you hold a low opinion of her, then she has no reason to want to be "in your life." It is always easier to see the faults in others, rather than in ourselves.

Taking full responsibility for the altercation doesn't really make anything different. If you said what you believed to be true, as you say you did, then there is no way to put a good face on it.

The only hope I can see for reconnecting with her would be if you could take an honest look at yourself and see that how your sister treated her boyfriend was between him and her, not really any of your business. Also, going around diagnosing people is kind of arrogant. Showing some humility about who you are might go further to really change things. There may be a streak of narcissism in you that you are completely blind to. IDK. Most of us do have a least some unattractive features to our personalities that everyone can see, except us. Has your sister ever spoken critically of you to point out your flaws. If she hasn't done much of that, then maybe your note could say you thank her for not shining the spotlight on your flaws. I'll bet that would have some positive impact.