A constant supply is inconsistent with an 'unexpectedly cut back' supply; I wouldn't expect a constant supply to boost violence if it's decreasing supply that's supposed to boost violence.

In the short term, demand for violence is effectively fixed, so decreases in the supply of simulated violence lead to increases in actual violence as a substitution effect.

In the long term, exposure to violence leads to desensitization, so demand for simulated violence expands to meet the supply.

Given two otherwise-identical societies, in which one strictly limits the supply of violent imagery and the other does not, I predict that the latter will (eventually, due to desensitization) have a higher demand for violence, leading to more actual, physical violence during blackouts.

I've heard it argued that the one time when large-scale censorship would be morally justified is if a "Langford basilisk," that is, an image which kills the viewer, were found to exist. What if there were such an image, but it only killed a tiny percentage of the people who saw it, or required a long cumulative exposure to be effective? What if, rather than killing directly, it compelled the viewer to hurt others, or made those already considering such a course of action more likely to follow through on it?

This isn't a fully-general argument for censorship of any given subject that provokes disgust; it's quite specific to violent pornography.