From a gameplay and historical perspective, by practically any barometer that compares the loyalty and unity of the English, Spanish, French, even Germany kingdoms, and then compared to Italy, clearly, it does not deserve a king title.
One might as well have give the German kings the title 'Grand Poobah of the Moon' for all the effect that they claimed a title which was only enforced inasmuch as the strength of their german kingdom allowed the illusion.
Yet in this case, it is important to remember how resistance to Germany really began.
When Mathilda of Canossa died, (The broad that starts with all those Italian provinces in 1066), she didn't have a random country cousin take over. Her vast lands were held in abeyance while the German emperor dithered about what to do with them, an act which eventually got him in hot water with the Pope.
Eventually, this helped foster the 'city state' culture, as vast swathes of Canossa's former holdings declared independence, followed by others from unhappiness with the German HRE and tacit support from the Pope. Yet the game does not model this change from Bishorpics to Republics by 1100, which is why I've modded them in my game to began as Republics.
Combined with the apex of the Norman power of Sicily whom the Pope turned to for an ally against the HRE, there was a window of about 50 years where the authority of the German kings was practically nonexistant. Without Sicily, the Pope would not have had the political strength to stake his own ground. After Sicily was disastrously lost through marriage to a German Prince in the late 12th century, (who later gave us Frederick Stupor Mundi, so can be forgiven), they lost this 'freedom of action'. Yet did not wise up to the times. A significant reason for the following century of conflict between Guelf and Ghibelline.
There would not be a systematic attempt to reinstate Imperial authority until Frederick Barbarossa in the mid-late 1100s.
And we all know how that turned out.