I don't think she was asking for independence. He chose not to fight the war that would have been required to keep the North in the Seven Kingdoms.
A Stark ruling in the North is a tenet of Northern nationalism. Lyanna Mormont supports Jon as King in the North because he has Stark blood. Sociologically, the North sees itself as distinct, with its unique history, separate religion, and its ethnic heritage coming from the First Men rather than the Andals. There is a notably xenophobic reaction when the foreign Queen comes waltzing into Winterfell with her foreign army.
I interpret Sansa as a character who moved away from sympathy for cosmopolitanism and multiculturalism due to her personal experience and towards a stance of nationalism.