There should be consequences for a Catholic ruler creating a non-HRE empire.

Empire was a complex concept in medieval Europe. A Catholic ruler claiming to rule an empire that wasn't the HRE seems like it would've been fairly shocking (borderline heretical) since "empire" was so closely linked to being the successor of the Roman Empire (which only the HRE was allowed to legitimately claim).

Ruling a non-HRE empire while the HRE exists should be a massive hit to piety, maybe, or carry a high chance of excommunication for you and everyone in your realm. (This kind of highlights how badly the game needs anti-popes and a religion rework in general).