I've got to disagree with you, Harry was made to be an auror. He's got everything a great auror (which he is) needs. For one, he's extremely observant, he always noticed all the little movements someone did and was able to connect it with situation (Remus pretending to read the book because his eyes weren't moving, Hagrid clutching his umbrella tighter at mention of his wand, Hermione having book upside down, etc.) Even right after waking up in Gof, he was able to say something bad was happening only by the sounds, he couldn't see anything when the dementors attacked in Ootp, so he focused on hearing them before he saw them.
He is also good at connecting the dots, he was the one who figured out why no one died from basilisk while basing it only on paper left by Hermione, he realized Bellatrix had horcrux in her vault by her reaction, and he realized Voldemort was after elder wand only basing on Xenophilius's story about Deathly Hallows (and that he's Ignotus's descendant).
Harry loves adventures. He thought that meeting Fluffy for the first time was a great adventure and was keen on having another one. He felt quite exited to break into ministry to steal the horcrux from Umbridge. He wouldn't be able to sit in a castle and teach children, he didn't even want to teach his classmates at first, and you think he'd want to teach hundreds of students same things over and over again and later check their essays? He wanted to become an auror ever since Barty Crouch Jr told him he'd make a good one.
He's great at DADA, Transfiguration, Charms, Herbology, and even Potions, getting an E while Snape is his teacher, and extremely biased against him, basically he's great at everything needed to be an auror. Not to mention he's quite powerful. His accidental magic was powerful, shrinking jumpers, somehow ending up on the roof of a building, and vanishing glass from a zoo exhibit. Not to mention he casted a full Patronus that drove away hundreds of dementors at the young age of 13, was able to stand up to imperious, even the one casted by Voldemort himself, and contrary to popular belief, he was really good at dueling, managing to do it even against Death Eaters.
Harry's really good at working under pressure, and even though his plans don't always work, his intuition never fails. The intuition told him to touch Quirrell's face, to put on sorting hat, to destroy diary and way more. He's brave, he's tough and works hard when the matter is really important.
Besides, do you believe McGonagall would let him teach when she literally argued with Umbridge promising to make him an auror if it was the last thing she ever did?
