I feel like when drogon burned the iron throne it was a message to the world and more specifically to jon : the iron throne always belonged to the Targaryens for it was forged by their dragon, now my Targaryen mother died and her family's legacy dies with her ; the last Targaryen; by the last dragon. Like he's telling Jon that he does not consider him as a Targaryen therefore he doesn't deserve to have that seat or anyone else.