Your premise is flawed. Neither The Wall or the Watch are a part of the North. They answer to no Kings and owe no fealty to anyone.
Before the Conquest, Watch was manned collectively by men of all the Kingdoms. It still is. It is the shield that guards the realms of men, it doesn't guard one realm and owes no allegiance to any realm. It serves everyone and protects everyone.
If you want an explicit example, Princess Nymeria sent her six rival Kings to the wall in golden chains once she completed her conquest and brought whole Dorne under the rule of House Nymeros-Martell. Needless to say, North as an Independent Kingdom existed back then and the Wall was definitely not in Principality of Dorne's control.
Of course as you say, Sansa can try and pry away Jon, and Jon can try to escape. After all, Aegor Rivers, commonly known as 'Bittersteel' was rescued when his ship en-route to the Watch was intercepted by his friends. But will Sansa commit such a dishonourable act? Brandon will be forced to enforce his will or his word would count for less. Will Jon be willing to do that? He never wanted anything to do with the politics and administration, he's going home for all he cares. And if Jon does desert or escape, Sansa will have to execute him/hand him back to the watch if he deserts, try to capture him if he escapes. Otherwise Stark honour means for less.
And What happens if the Word reaches the Unsullied that they were played for a fool and their Queen's murderer now sits beside his sister in Winterfell? You can expect Yara Greyjoy, who sided openly with Greyworm, would definitely make sure that the word does reach them. With Ironborn descending from the West and Unsullied from the East, North would be smashed even if Bran takes no hand. Doing so will also give Yara the allies she needs to win her independence with fire and steel after Sansa tricked them all into accepting her brother as King, in case she resents that and wishes to fulfil her father's mission. Giving Jon refuge will:
- Dishonour Starks
- Make Sansa look weak and unjust
- Put the North in risk of a conflict with the Six Kingdoms and the Unsullied.
And you forget, as Tyrion said, Half the country hates people who betrayed Daenerys. Jon would always be at risk of assassination down south by Targaryen loyalists.