Some thoughts, 12 hours later.
1) Attorney General Grey Worm. Rather than execute mutineer Jon Snow, Grey Worm imprisons the killer of The One True Queen: Grey Worm's liberator, leader and mother figure, beloved by his own late beloved. He has the presence of mind to see that in this incinerated city -- now without its incinerator -- his armies are vulnerable to a siege led by the armies of, well, everyone else. Jon is bound over as a hostage in negotiations with the forces that include his three other family members.
Meanwhile -- more inexplicably --- Grey Worm keeps the Imp on ice so that Tyrion may be judged by...Dany's successor as ruler of the Seven Kingdoms? Who has yet to be decided, but will be, in a vote that excludes Grey Worm? A vote called, debated and ratified in whole by the prisoner himself?
2) The Night's Watch: was this more cleverness by Tyrion, banishing Jon to what Tyrion knew was, in fact, a reunion with Tormund, Ghost and the Free Folk? (An exile enforced by Sansa on the throne of the North -- the only kingdom which now borders the Wall?)
3) Drogon survived to grieve, melt the Iron Throne, and forsake Westeros for a home in the East. My theory: when he touched Dany's body, a trace of her spirit merged with his. He destroyed the throne because it, more than Jon, had been the ruin of her. Yet also to assure that no one else -- neither Targaryen nor usurper -- would sit on it in her stead.
Agree with Direwolf Pup that Drogon returned with Dany to their homeland of Valyria, where among the half-living stone creatures, Drogon rules in all but name.
Jon was the true heir to nothing, from the moment Aerys and Targaryen rule were overthrown in Robert's Rebellion. But anyways. Jon had already yielded to Daenerys both his title as King in the North and his pretender's claims to the Seven Kingdoms; he likely surrendered to Grey Worm as Jon Snow. His being banished was the terms of his release; those terms ended the siege and resulted in the Unsullieds' departing Westeros.
Indeed, even with Drogon drowsily on guard. But let's say that Dany chose to be alone for this first encounter. (Good timing, Jon!)
What if Jon had chosen to approach her unarmed: to protect her from his doubts, as well as lull her own? Then in extremis, done an Arthur and pulled a sword out of the throne? Or was this the time to continue dialing back on the supernatural and on the theme of Jon, the predestined hero?
No one likes a wise guy. Especially showrunners making a lame joke.