I've seen other stuff in fiction that makes hellhonunds cool. Gives them hellfire powers or other stuff. Makes them dangerous and stand out. In canon, Hellhounds for Hazbin are furries? I'm not getting the demonic bit here. What makes hellhounds stand out? Is Luna a shadowhellhound?
Now, Lucifer and his other selves are powerful but there are other fallen angels, sinner overlords, demons that if working together could rival his power. Want to keep that sense of conflict, and Hellhounds are boring.