His becoming an Auror made no sense. McGonagall pressured him to think about what he wanted to do in the future in his 4th year to plan out the rest of his education. Auror was his very first idea, and he wasnt really even super into the idea then. It seemed to be mostly out of a sense of admiration for Mad-Eye Moody specifically. And then, despite finding out that Moody was in fact a Death Eater trying to kill him the whole time, somehow that didn't taint his opinion on the Auror thing at all.
Even though it was just the first thing to pop into his head, he never gives it any sort of critical thought or even comes up with any alternatives. He doesn't even have an understanding of the greater wizarding world at that point to even know what kind of work exists outside of Hogwarts and Hogsmeade. He just shrugs and goes with his first idea anyway. But then he's not even committed to that idea really. He is not even bummed when his grades would apparently prevent him from taking Advanced Potions, a required class to become an Auror. When he learns that Slugorn had less strict requirements and he can take the class after all, he's just kind of like, oh okay... "guess I will keep following this path. I have no other ideas."
I agree with the Carlin Brothers that his career after Hogwarts should have been at Hogwarts. Whatever admiration he had for the fake Moody, the real Moody, or both, his truest admiration was for Dumbledore. And Hogwarts was his first real home. He excelled at Defense Against the Dark Arts from the beginning, and by his 5th year was even already teaching his classmates (including older students) skills that he had. And he was an incredibly effective teacher too, with his students using the skills he taught in the fight at the department of mysteries and the battle of hogwarts. He had more experience by then end of the 7th book fighting Dark Wizards than most Aurors at the ministry would have. That job would have been boring as hell after Voldemort and the Death Eaters were defeated. But he could use his experiences to enrich the next generations of witches and wizards, teach them to protect themselves, and be there to make sure Hogwarts remained the haven that is had been for him. It makes WAY more sense for him to have become the Defense Against the Dark Arts professor (especially since he broke the curse on the job with Voldemort's defeat). But then count on JK to do some stupid shit.