Again, as everyone else, you are welcome to prove me wrong.I'm sorry but your three core traits boil down to playing a murder hobo and that doesn't set S&S apart.
If you have examples of stories that feel like Sword & Sorcery and that have protagonists who are well integrated and influential people in their society and its institutions, who feel obligate to a duty to the public or loyalty to a lord, and who make attempts to solve conflicts through diplomacy and peaceful means, or delegate the dirty work to others, then I'd really be happy to hear them.
Conan becomes king, but he's not accepted by the people. Fafhrd and Gray Mouser are self-absorbed leeches. Elric may have a crown, but is exiled from his Empire in everything but name. Kane is the boogyman.
Now Jirel can be assumed to be well respected and beloved as ruler of her domain, but all the stories take place away from her people so none of her status is of any use on her adventures. And she also descends alone into nightmarish realms with a sword in hand. I believe the same applies to Bran Mac Morn.