>>513087575
More or less so, Rome became a religious seat on its own right but couldn't quite impose its will directly on much territory
>>513087580
>As I already pointed out that was only really the Hohstaufens, and that failed,
So once HRE emperors realized taking back Italy was unfeasible they stopped trying to do so directly (prefering instead to wage proxy wars via the ghibellines, who were also defeated) until the occasion arose again centuries later in the Italian wars. Seriously, I can hardly think of anything more definitive than the string of defeats the HRE cumulated in Italy during the Low Middle Ages- direct intervention from the North failed, attempts to reconquer it from the South via intermarriage with the Normans also failed, proxy wars via ghibellines failed. For an empire that allegedly didn't really care about the autonomy of Italian polities, they sure tried to quash it quite a lot before giving up lol.
>in the same circumstances as most of Germany
Wrong, again unlike German ones, no Italian polity partook in the imperial election, diet, courts like the imperial chamber court or aulic council etc. None of them was under Imperial immediacy. Imperial laws did not apply to them. None of them was legally bound to levy troops for Imperial campaigns. For example, while most HRE German states took part in the aforementioned Hussite wars, Italian city-states didnt.
>the HRE was just trying to keep France from taking over Italy.
No lol, they were actively trying to take back their former land, particularly within what today we'd call the Triveneto area- in the case of the city of Trieste they actually did succeed for once, as we only took it back a little over a century ago.
I think this just boils down to the fact that, unlike here, they don't really teach you Italian history in detail down in the States, understably so, so you end up trying to fill in the gaps with MSpaint maps and stuff like that.