So, here's the thing. Yes, the story "starts" in TPM as he leaves his mother. You can see the a-to-b-to-c of it. But is it effectively handled? No, not really. It's the difference between me saying "Anakin does X, then Y, then Z" and actually taking you on the emotional journey in a way that paces the communication of that story effectively. I don't think the PT is well paced or well told at all, although the core idea is...ok-ish. Not what I'd prefer for his motivation, but at least it basically follows.
The direction, performances, and script just don't really carry the journey effectively. It's the wrong mix of "show, don't tell" and "don't show or tell, but say what you were trying to do after the fact in an effort to clarify." And yes, when you say "Anakin and Obi-Wan were brothers. Qui-Gon was a father figure that was taken away from Anakin early on, and Obi-Wan couldn't fill his shoes, and then Palpatine did and turned him to evil," I can kinda see the outline of that in the films. But the fact that you have to draw a big highlight around that after the fact rather suggests that the message wasn't all that clear early on. Plus, it doesn't exactly map on to the earlier interpretation which is about emotional repression and unresolved separation anxiety, which I think are far more front-and-center.
I think a huge amount of that is the fact that they take so much time to do TPM. As a story on its own, TPM is...fine, I guess. Jar Jar is stupid and annoying, and much of the design choices were underwhelming. But if it wasn't part of the saga, and was just, like, a two-part episode of "The Clone Wars" or something, as some flashback, it would be ok. But as part of the overall saga? It's a massive waste of time for the story you're trying to tell. It could be handled in exposition in other films that instead spend their time showing Anakin's state of mind during the war, and then tying that much more effectively to the fall of the Republic itself. The gradual embrace of totalitarianism, all in the name of ostensibly doing it for higher purposes, grasping for quick and easy power in an attempt to solve some problem but corrupting yourself in the process, etc., etc.
But when you're limited to about roughly 7-ish hours to tell your story, man, you ain't got time to dick around with kiddie-Anakin and his super fun adventure going pod racing. Like, seriously, probably about 1/4-1/3 of TPM is devoted to getting off Tatooine. And it doesn't matter. Most of that stuff is totally irrelevant to the larger story of Anakin's fall. The same with all the Jar Jar fart jokes. Those are all just...things that happen, and you only arguably need to show them because something happened before them and if you don't show them then it raises a question of "But how'd they get out of that?" when the truth is NONE OF THAT STUFF MATTERED, or rather only maybe 20% of what was shown matters to the overall story.