During the episode "The Impossible Astronaut," we see the Doctor get shot by River Song. He starts to regenerate, but then he gets shot again, killing him. But including the war Doctor, the Doctor had used up all of his regenerations, so how is it possible for him to regenerate? We know he was inside the Teselecta and that he didn't actually die, but if he did die he wouldn't have regenerated. My question is, why bother to fake a failed regeneration that couldn't even have happened? Why not just fall to the ground?
In-Universe: The Tesselecta didn't know about the regeneration limit and The Doctor never bothered to tell them, or anyone for that matter, until he revealed it to Clara in Time of the Doctor. As a result, when they were "shot", they acted as the real Doctor would have (given the information they had on file), mimicking the process of regeneration before it was interrupted by a second shot. His companions, especially the River watching, would have been suspicious if he hadn't started to regenerate.
Out-of-Universe: Moffat, as usual, didn't think that far ahead. Part of it was that "The War Doctor" wasn't even a thing in 2011 (when those episodes would have been written), since the BBC were still hoping that Eccleston would come back for the 50th anniversary special. After it became apparent that he wasn't going to forgive them that easily, 'The War Doctor' came into being.
Another part of it was that nobody even bothered to think about it until Matt Smith announced his intention to leave Doctor Who, at which point fans started making the point of "Oh, but he's hit his limit, because War Doctor and Tenth's 'extra' regeneration".
It could easily have been written that there is no limit, or that the limit is bigger than 13, or maybe even that Tennant's "handy" extra regeneration didn't count, but instead Moffat decided to write every piece of fan speculation on the internet into the show as hard fact.