Stannis has no power over the undead, Jon Snow does.

I literally never thought for a second that Stannis would ever sit on the Iron Throne. I thought he'd play his part on the Wall and maybe against the walkers and the Boltons, but ultimately he's one of those characters who is there to serve a purpose and die as soon as that purpose is served.

I think if it were otherwise, we really would have gotten more into his background and his connection with his family, men and other real contenders for the throne and their agents (say, Littlefinger or Tyrion).