So if one’s intention is not to assault somebody with said rifle, why would we use terms that label it with that intention?

The terminology has been that way since the "Sturmgewehr 44", and since the US Army when they codified the term by defining it was such in their own texts. "Assault rifle" (not "assault weapon") had nothing to do with vilifying gun owners. The "assault" in that term is about making an assault on a position or any an event, as in an attacking advance or maneuver, not as in committing assault against a specific person. Put another way, it's a "storming (sturm) rifle", not "murder rifle".

You can use Modern Sporting Rifle, but I think you do more harm then good trying to avoid any terminology that references like "assault rifle/battle rifle" even when they're accurate to established norms, or refuting the "weapon of war" label. I even see people dislike referring to their own guns as "weapons". The reality is weapons of war, arms, are exactly what the 2A is meant to protect. It's okay to be unapologetic for the context that the weapons for designed for, even if your intention is just or defensive.