Germany and Italy were pretty much divided realms. Of course, you had many contacts and sometimes union between german and italian principalities, but they most generally didn't lasted.
Unfortunatly, what was possible was the political alliance between germans and italians against the emperor, along their own interests.
The problem, well problemS, with Imperial Italy was it was really really divided.
To begin with, when Germany was divided along roughly unified and strong duchies, Italy knew a similar fate than southern France with a really important feudal political desintegration; making any tentative to impose an authority complex at best.
Then, papal proximity made plays of power in Italy rather hard to maintain; dividing even deeper the Italian policies (pro-Imperial, pro-Pontifical, pro-themselves, etc.)
Simply said, Imperial Italy was hard to maintain of its own, not even considering the troubles happening only in Germany. At some point, you'd have either sort of formal vice-king (maybe the Kings of Romans), or an outright abandon.
In the former case, Italians emperors are even less odds to happen.