I agree with most of your comment, but is he really lazy about studying? We see him researching stuff a lot--exploding heart spell in Storm Front, vampire cures after Grave Peril, etc. In Skin Game, while fighting Hannah Ascher he rhapsodizes about loving the Art and spending time on it, as opposed to just liking the power of it.
I agree with that also, but by his own words, Harry says he was lazy about studying. Not until Molly becomes his apprentice that Harry starts to really apply himself. In Storm Front a lot of his knowledge comes mostly from Bob. Harry may of been mostly referring to his younger self, but that as you know is a critical foundation. Like a lot of very bright kids, they don't have to work hard to get by in their studies, so he didn't. Not that it was all Harry's fault, what Justin taught him he learned well, but Justin's education of Harry was limited to what Justin eventually wanted to turn Harry into, an "enforcer." However things like Latin, important for a wizard of the White Court, right? Harry was capable of learning it, but more often than not he cut class. Hell, he had no clue that the White Court even existed, so why learn a so called dead language? When he lived with Eb, it was mostly ethics that he learned and hard physical farm labor. Why? Maybe partly out of Eb's own guilt about driving his mother away by pushing her, but also in my opinion to keep Harry safe. Because young Harry had that much potential talent, and the Council was already terrified of him in many ways. So Eb kept many doors to knowledge closed to Harry, as did the Council apparently. Remember the comment about parts of the library at headquarters being forbidden to him?
Since Molly, Harry has applied himself, take veils, when we first meet him they are rudimentary at best, he complains he has no talent for them. That might be true, but when he starts training Molly who has a natural talent for them, he applies himself and by Battle Front he can pull off a decent one. Same goes for the Latin, he isn't comfortable with speaking it, but it is passable now.