I think the essential pieces of Anakin story from The Phantom Menace, being found by the Jedi and separated from his mother, should have been handled more concisely, perhaps in a prologue, and then have the story of the clone wars began in the latter half of the first movie.
Maybe, but then what's the emotional through-line for 'Episode One' going to be? Part of the problem here is that not only does the overarching story need to be served, but each instalment needs to be a complete and self contained story in and of itself.
You also have to come at it (as Lucas did) with the assumption that this is also going to be the first Star Wars movie a large proportion of the audience (mainly kids) may have seen, so it also has to introduce the world and set the stage.
If it was me, I would have jumped right to the start of The Clone Wars in the first movie, and then done a movie set in the middle of The Clone Wars as Episode II.
I think most of the important stuff about Anakin and the Jedi can be covered in exposition or the opening scroll, and the Anakin/Padme relationship could still work with a little tweaking to make the meeting in her apartment the first time they meet. It wouldn't have the 10 year crush, but I think it would still work out OK if Anakin's feelings for her started right there.
Can you imagine what ANH would have been like if every thing about Luke growing up on a farm, finding the secret message in a droid, meeting a wizard, finding out his dad was also a wizard, having his aunt and uncle die, meeting a space pirate and rescuing a princess from an evil sorcerer's fortress was all just in the opening crawl and it just dropped you right into the action with them escaping the Death Star?
You need that slow ramp-up to introduce your characters, set the stage, establish some kind of emotional connection between the audience and the protagonists. Otherwise it's all just a bunch of incoherent noise.
Part of the problem with the PT is that there's really too much ground to cover in just three 2 hour kid's movies, which is why AotC was such a rough ride. Lucas knew this and even contemplated making it four movies instead of three: 1) A prologue (basically TPM), 2) Ep1: "Clone Wars Part 1", 3) Ep2: "Clone Wars Part 2", and 4) Ep3: "Epilogue" (again, basically RotS).
Only he can say why he chose not to go this route (probably because it would've taken a decade to pull off and he didn't want to spend that much of his life on it) but ultimately, the movies aren't really about the Clone Wars, it's Anakin's story so that's what he hewed to.
Thankfully the Clone Wars show did wonders to flesh out that period and help add a lot of context to Anakin's story that the movies simply didn't have time for.