Really, "the power of legitimate violence" doesn't compute. If someone has the actual power to use violence against the population, what difference does it make

Really, "the power of legitimate violence" doesn't compute. If someone has the actual power to use violence against the population, what difference does it make whether it is somehow nominally illegitimate? Giving all the power to private corporations is not a solution to that problem, because then those corporations ultimately will also end up with the power to use violence. Your only hope is to keep power distributed.