While Jamie is a nepo baby, the story reinforces her exceptional ability. Yes, one could argue that Jamie clerked for circuit and SC judges after graduation because she's a Carrington. However, the story clearly indicates she likely got those roles because of her exceptional ability - top of her class at Harvard and wrote an opinion less than two years out of law school that will probably be adopted as a standard by the courts.
The story also suggests Jamie wants to obtain her goals based on her abilities, despite being a Carrington. Witness those occasions in the dialogues where Jamie gets annoyed when Rockford labors the point that she's a Carrington. Never once has she thrown her family name around.
You are right that her family name offers opportunities others would dream of, but I get the impression she mostly wants to achieve her goals through her abilities, not by using the family name.
