Your statement that you thought some of Episode III's plot should have happened in Episode II really forms the core of my argument for why III may possibly be the worst of the three prequels, despite everyone saying it's the best:

It tries to do everything that all three prequels should have done, in the span of one movie. I and II are almost entirely unnecessary. Anakin's turn should have happened at the end of II (or we believe Anakin dies at the end of II), and III should have revolved around the repercussions of this, the rise of Darth Vader, and the beginning of his Jedi extermination campaign.

Instead, we got all the events that should have happened during the course of three films that span many years, happening in two hours over the span of, what, a couple weeks?