Bolstering my earlier argument, Brian Palmer provides some relavent evidence.
According to data compiled by Grant Duwe of the Minnesota Department of Corrections, guns killed an average of 4.92 victims per mass murder in the United States during the 20th century, just edging out knives, blunt objects, and bare hands, which killed 4.52 people per incident. Fire killed 6.82 people per mass murder, while explosives far outpaced the other options at 20.82. Of the 25 deadliest mass murders in the 20th century, only 52 percent involved guns.
The U.S. mass murder rate does not seem to rise or fall with the availability of automatic weapons. It reached its highest level in 1929, when fully automatic firearms were expensive and mostly limited to soldiers and organized criminals. The rate dipped in the mid-1930s, staying relatively low before surging again in the 1970s through 1990s. Some criminologists attribute the late-century spike to the potential for instant notoriety: Beginning with Charles Whitman’s1966 shooting spree from atop a University of Texas tower, mass murderers became household names.
Emphasis mine.
Again, eliminating one means of satisfying their actual end will not put an end to, or reduce the incidences of, mass murders. If the end is notoriety, then only after the media stops satisfying it are we likely to see a reduction.

