But obviously part of that is the ubiquity of guns. If you're a criminal in America and you want to get an illegal gun, I'd imagine it's much cheaper and easier than it would be in any country where it's banned. You're also presumably less likely to get caught until you use it, because simply having a gun is not necessarily a reason to get stopped by the police. A quick Google suggests that illegally purchasing a handgun can be as little as a fine of up to $1000. That's presumably because you have to include people who just didn't do their admin correctly, as well as people who obtained them for malicious reasons.
In the UK, it's a minimum sentence of 5 years, up to 10 years, and up to life if other crimes are involved. The argument you often hear, that 'the criminals would still own them' is simply not an argument that stands up for all but a tiny minority of serious armed criminals. For anyone else, the expense, difficulty of obtaining them, and massive risk of actually using them simply don't make sense on any level. In a country where no-one else owns a gun, you might as well just get a knife from your kitchen. Which is what a lot of them do, hence the knife problem. But I'd rather have a knife problem than a gun problem, to be honest.