I think it suited well that it came so late into the season. This Doctor more than anyone has to find out who he is by doing and being, and so do we the audience. This Doctor is said to be the 12th when in reality he's the 13th and the First in a new series of regenerations given to him at a time when he was convinced he would be dead.
The 11th (12th) had come to peace with his passing, having lived and fought well beyond what would be considered reasonable by any definition of sanity, and then all of a sudden he was, unexpectedly, given a next life.
The previous Doctors have had small similarities to their forebearers as their strings of lives, even though new and different, still was a continued and expected event.
The 13th regeneration is something unexpected, with the Galifreyans themselves having broken the rule they set up themselves, probably for a good reason too.
The 12 regeneration rules have been shown to be able to be broken. That means it was a rule rather than a natural restriction. We have no idea of the proces behind this rule, though if the behaviour of the 13th is any indication, it was most likely a very well thought out rule.