Your first three paragraphs are well written and smack of good, rational thinking. The second two paragraphs are well written, but are a different narrative than the first three. It is important to note that crazy people are still well versed in being crazy even in nations where compulsory weapons training is endemic. You effectively say this in your second paragraph, even though you make the point about being lone.
the problem comes when the guy carrying a dozen handguns is the only guy like that in a crowded place when he snaps and decides to go all murder-happy.
It's also important to note that even in well versed and trained military scenarios, when a lot of people start shooting, innocent people start dying (e.g. Pat Tillman, the many civilian deaths in Irag/Afghanistan/etc...). I would argue that there is no credible evidence or example scenarios for the "give everyone a gun and some training" to make us all safer postulate. Imagine the carnage if everyone was shooting back on the south side of Chicago these days. Plus, the Aurora, CO shooting should prove that making it legal to carry weapons isn't a solution (to an extent). In CO, it's legal to carry concealed firearms, but no one in the theater was, or they didn't want to use them. And to be honest, the last place I want to be is where it's entirely possible that there are multiple shooters in a dark room with lots of noise and confusion. I think it can be argued it's at least possible that a lone shooter resulted in fewer deaths than otherwise may have happened.
The biggest problem here is that most of this is assumption and based on personal feelings. In the end, nothing really changes one way or another. So like all the deaths due to drunk driving (we certainly aren't going to give up alcohol, and most don't really care that much), we should just accept that people are going to die like this every now and then, let it happen, and move on.