What the do-gooder's fail to realize is it really has nothing to do with guns, rather the breakdown of society.
People(all people) are most comfortable in small groups of similar nature. When it was villages and towns, murder was rare. People also cared about their neighbors well being, if for no other reason than it directly affected THEIR community.(why do you think service clubs began forming as cities got large?)
The bigger communities get, the more fragmented people get, and the less they care about each other. In a city you commonly drive by someone having car problems. In a rural area, you don't.
Fragmentation of core groups soon leads to feelings of alienation, loneliness, frustration; and there lies the problem.
Doesn't matter wether it's random gun violence, or some other form of personal attack, if the instigator had the feeling of belonging to a core group, and the support(or even guilt of doing wrong against it), this type of thing would be extremely rare.
Then again, the odd person is just simply wired wrong, and will never fit into any society. Trying to sort these folks out is a waste of time. That, I think is the REAL reason to have a death penalty. Think of it as a last resort cull.
So; no, restricting guns won't make a damn bit of difference in the long run. Next it'd be knives and crossbows, soon we'd be banned from using forks.