I don't really disagree with you, but I do perceive a serious problem. Who is to say what the difference is between a riot and, say, the Whiskey Rebellion? Further, once a force is equipped to stop rioting or rebelling mobs, will they not seek out justifications to use that equipment, thus expanding and encroaching power in the exact way we all (supposedly) hate?
Finally, I would add that in the original Framer's model the quelling of such mega-riots would have been handled by the local citizens on the ground in their capacity as militia, and then the riots would not be quelled so much as property being protected from damage or looting, and let the riot run it's course.
Sociologically, it is always healthier to let outrage run it's course. It's when you try to bottle it up that it turns into a pressure cooker.
If every able-bodied soul were armed and had some experience at the militia, then the Mayor could have said, "A destructive riot is now in progress. All measures are authorized to the unorganized militia to defend against theft and looting. Unauthorized trespass will be considered intent to loot." you could lay in a covered defense behind storefronts and just drop anybody that breaks in. pretty soon everyone else will get the message: riot all you want but break into property and you die. It won't be long if that becomes the common practice, where people riot all the time with almost no real property damage. Which frankly would be fine by me. Let people outrage. It is their right as Americans. Don't let them destroy people's property when they do.
IF we had a proper unorganized militia, then the actual police would only ever need to get barely over Andy Griffith. For anything really big just co-op with the local militia which would do the double-duty of ensuring that said action(s) had the real sanction of the public.
We of course do not have such a thing today, and in this age the question of what to do in an actual destructive riot is a lot more perplexing. Asking to police to quell riots (put down insurrections) is pretty much equivalent to asking for encroaching abuse and eventual tyranny. Until we can fix the underlying problems in the balance of power, perhaps a bridge over the gap would be deploying the National Guard in a "defense of property only" role with a similar ROE to the militia I described above.