It's also got a lot to do with stuff that isn't crimes. Easy gun access is more or less getting a lot of people killed or injured with no crime involved. Suicide and accidents are the big ones, particularly the former, and it's... pretty safe to say making guns harder to get to cuts down on both of those quite noticeably, and in particular makes suicide significantly less likely to be successful.
Crime wise, another pretty substantial facet of it's just because in societies that don't have the rampant proliferation that the US does, you're... probably notably more likely to survive encountering violent crime, and come out less injured to boot, even when it's not just flat out less likely to encounter at all. Buncha' other stuff besides, of course.
There's not really a single reason behind most of the more reasonable gun control advocates (which is to say most of them, generally) advocation, basically. There's a fair number of things we're pretty sure at this point that getting firearm saturation (among other things related to gun control) to a more manageable level would improve the state of things in regards to.
And that's just talking about potential legal changes and whatnot. There's an entire other fight to be had in regards to enforcement, which... is not in a good state in the US. ATF et al are basically crippled in most places in this country, last I checked.* S'been a few years since I did, so things may have improved, but... yeah. US would probably be doing better on the firearm related fatality/injury front if we were actually fully enforcing the laws we already bloody have, nevermind actually introducing changes to them.
*E: Anyone know if that legal mandate they had to not digitize bloody anything related to firearm records and whatnot was ever lifted?