That's not what Imperator meant in republican context, and that's not the title he regularly used. Imperator meant someone who is invested with imperium, and thats literally it, varying from a governor, to a general, to a high level magistrate, etc. It's true Egypt had one after Imperial integration, but your supposition as to why is a bit erroneous. It was used because literally anyone in control of a province had to have Imperium, and anyone with Imperium was Imperator. Imperator took on a different usage throughout the empire especially after the crisis of the 3rd century, and that's the one you're using. Augustus generally used the titles of "Princeps", "Pater Patriae", or "Caesar" as even by his later life it had taken on a political sense, not just a reverential one.