darthfanta, Karolus Rex, the main problem with all this is the order of prestige and precedence. Italy has more tradition, more culture, more urban civilization and simply more wealth than Germany. In religious times, it has so much more holiness. The on ething Grmany is better in (in these times) is organizing a cohesive fighting force. Which usually works for keeping Italy down enough.
Having your heir rule over Italy while you stay in Germany will be strange, but leaving Italy once you have reached the imperial title? That might have practical reasons, but I really contend that the people of these times will not be able to see that logic.
I am rather sure that under such a scheme, the first Rex Romanorum will "go native" in Italy. Once his father dies and he can get himself crowned as emperor, he will realize that under the new system, once his son grows up and he gets old and sickly, he will have to leave the sunny shores and palazzi of Italy for cold, grey and rainy Germany. Forever.
I mean, Frederick II. did grow up in Italy in OTL and while he did not give up his power over Germany, he did not like to go north of the Alps, either. And why should he?
And the opposite model - the ruler in or near Rome, the adult heir in Germany sending support and supply, did not work well either.
Taking the pope hostage has its practical problems as well. Aveignon was surrounded by France, but it was not French, it was a papal possession. There is no place in Germany that has nearly the historical clout and prestige to house the Bishop of Rome (and he is pope just because he is the bishop-patriarch of Rome).
What I could see: One emperor taking tha current pope back to Germany to ensure the coronation of the next emperor. But once that Pope dies, where are the cardinals? Also in Germany? You cannot tie them down perpetually. It needs just one cardinal and a rival ruler and there will be another pope and probablyx another emperor. Because the German pope and the German emperor will lack the universal prestige if they`ve never been in Rome.