The Early Middle Ages were not kind to Rome, and the long destructive war to recapture it didn't help things. By the time the dust settled, Rome had practically ceased to exist as a major city, with population estimates ranging from less than 50,000, to a tenth that*
The rest of the peninsula didn't do much better. According to McEvedy and Jones, Italy was near its lowest population in its recorded history at that time (and would hit it around 600AD). So its not like there was a huge latent reservoir of Italians waiting for a good chance to move back to Rome either.
Constantinople on the other hand was at a population high point, somewhere in the vicinity of 300,000 to 500,000 people* (prior to the Plague), making it far and away the largest city in Europe. It wouldn't surpass this level again until after the Turks captured it.
So there wouldn't be much value in moving to destitute Rome from rich Constantinople, and anyone an Emperor left behind to manage the great city after he left would control so many more resources that the tail would capable of wagging the dog.
Yes, an emperor could try to rebuild Rome, with an eye toward perhaps making it capital-worthy in the future. There's even some indication that Justinan was doing the former (if not shoot toward the latter). However, there was only about 16 years to work on that project before the Lombards invaded.
* - I personally tend to lean toward the lower numbers. Sadly, the graphs I could find online seem to prefer the higher ones. However, they should have the rough trends about right, if not the y-axis values.