I think the point that Jason, and I with some of my complaints, are trying to make isn't that there's no narrative way around it, it's that they haven't given us one. Jon being a Night's Watch deserter would be a big deal to people in the north, especially now that the army of the dead is marching. But basically nobody has even brought it up, and again, killing a deserter is the first thing we saw Ned do, so there's no way Ned's son (for all anyone knows) would desert the Night's Watch. Somebody would bring it up, and nobody has.
If nobody cares, what's to stop everyone else in the Night's Watch from abandoning the wall to return to their families/do whatever they want. It would be a big deal.
Now, there are all kinds of narrative ways around it they could have come up with, but they chose "just ignore it and hope nobody notices." Again, the small things helped make this show, and this would be more than a small thing.
It's the same thing with the ridiculous Arya/Sansa thing with the letter.