Calling the police's capacity for violence merely "the right to self-defense" is absurd. Qualified immunity goes so far beyond the rights of normal citizens that there really is no possible comparison. Not even the fever dreams of the most radical libertarian encompass qualified immunity for civilians.

The police in the United States are a paramilitary force, equipped with military gear, and in many cases with military training -- the only thing military thing they don't have is the uniform code of military justice, which forbids things like the use of chemical weaponry and war crimes.