The North have a large army. Could they not just march south, offer Jon his kingship in the North, and be fine? His "brother" is the king and I doubt the Unsullied would start a war over a king in a separate kingdom.
There's issues besides the Unsullied. Primarily among them is that Jon's real identity is known to several people, and if that gets out it could put him in danger simply because someone might decide there's too much of a risk the last Targaryen could make a play for the throne, however much Jon doesn't want the job, just as he didn't want to be King in the North but ended up being forced into the position by circumstances. The fact that Drogon is still out there, and Jon has been a dragon rider, would only make people even more paranoid.
What Jon's allies did was, in fact, a successful con job. By sentencing him to the Night Watch, they removed him from any claim on the throne thus no one would have reason to see him as a threat. And most people don't know that he was happy (before all hell broke out) living among the Wildlings in the far north, and given the events of the series, the survivors there are utterly loyal to him. They, basically, put him somewhere where he could simply walk free into the life he wanted, away from all the politics and the bad memories, and live among people who respected him.
The idea that the Wall is breached and people could simply walk north and not be in danger of being killed right away, so being assigned to the Wall is not, in fact, a prison sentence, isn't something that people in the south would understand yet on a gut level. They think they've tossed him into a glorified prison.