I just don't think rates would go down because 1) accidental gun injuries are very low, and account for very little of the cost of homeowner's insurance. The money paid into those policies mostly covers things that are much, much more likely to happen, like natural disasters, crappy craftsmanship, or fire. 2) Insurance companies....lowering rates? Lol. If removing guns did lower the policy by, idk, $5 a month, which is negligible, they would probably say there is no point in lowering prices since the decrease is barely noticeable, and most importantly (for them), people are already used to paying the original price.
A pit bull would make your insurance go up more than a gun, but like I always say, it's not the dog, it's the owner. Same thing with guns. If you're a psychopath, you might kill someone....guns don't go around killing people on their own. However, if you're a psychopath and dead set (no pun intended) on killing someone, you're going to do it with whatever you can get your hands on, be it a gun, a knife, a pencil, a screwdriver, a hammer, etc. Or yes, even a car. However, I think you agree it would be absolutely ridiculous to ban all of those things just because they can be used to kill someone. Lots of serial killers don't even use guns.
I don't think anyone experiencing acute psychosis should be doing anything but sitting in a padded room. I have to disagree that people try to avoid danger though. Not only is there the whole "extreme sports" thing that it seems like everyone is into, but most people's attitude on dangerous things is, "hey, this might kill me...then again maybe not". If people tried to avoid putting themselves in dangerous situations, no one would ever drive anywhere.