Well, that's an interesting idea, which certainly seems to kind of fit what is presented by the original Star Wars. The only thing that kind of works against it is the fact that Obi-Wan remembers the Clone Wars and that the last remnant of the Old Republic, the Senate, was swept away as part of the timeline to the film.Something I think would have improved the prequels, and in addition to the originals in my opinion would be to extend the rule of the Empire hundreds, perhaps thousands of years into the past. That eliminates the prequels need to show the rise of the Empire and just show the fall of Anakin and the Jedi. It also makes the plight of the Rebels in the originals that more dire, knowing they are going up against a system that has existed for a long, long time, and not one that rose and fell in only a few decades, which is only a blip compared to the scale of the thousands of years the Republic lasted.
One place I think that the PT succeeded is that it showed the Grand Army of the Republic and its capabilities, giving insight in to what lays the foundation for the Imperial war machine.
That said, I think that having the Empire appear earlier in the PT might be more interesting, and give a better sense of scale of how large the Empire truly is. Which, as much as it's cool to see a huge Senate building, it feels all kind of too big for me to identify with.