If it is those "who use a gun to steal, maim or kill without any provocation that is the issue" then it is not "a couple of dozen mentally deranged individuals" who you need to address but the most basic building block of society itself - the family:
FBI
53.0 percent were killed by someone they knew (acquaintance, neighbor, friend, boyfriend, etc.); 24.8 percent of victims were slain by family members
http://www.fbi.gov/about-us/cjis/ucr...elatesmall.gif
The "random" attacker isn't the one you need to address as first priority, rather the people in your own household. By providing guns for "self-defence" you also provide the necessary means for people who live under the same roof to kill each other.
What's next? A husband and wife to have separate guns on either side of the bed so that they can defend themselves against each other? Sure the picture is stretched to incredulity with hyperbole but it illustrates the bulk of the problem.
You don't believe that it's a reasonable solution because you accept people being slain as a necessary trade-off to your "freedom".