As I understand it, research suggests that most desires to kill are temporary - moral philosophers might say that they aren't reflexively stable, behavioral psychologists might say that people are easily put off by trivial inconveniences.

Regardless of the causal mechanism, the evidence is pretty good that unavailability of highly effective weapons prevents both random and unrandom murders. Thus, weapons limitations are likely to be relevant to all kinds of murders.

Even if that isn't true, random murders are so uncommon that designing interventions specific to them is very similar to focusing medical research on curing the injuries people suffer only when struck by lighting. In short, probably a waste of attention in terms of marginal improvements.