Is the fear of a ban on all guns in the US irrational? Probably, I agree. But that's about the extent of it. You acknowledge some restrictions will lead to more restrictions until we're satisfied the problem is remedied. My belief, based on pretty sound reasoning, I think, is that the problem won't be remedied, if at all, until we get to the point of severe handgun limitations/bans/confiscations.
And that's irrational nonsense, because to use a common phrase, 'the cat is out of the bag'. You can't do a total blanket ban as they are simply too common - it'd be like prohibiting alcohol, it simply wouldn't work.
Instead, it'll be to the point you solve the issues that your society has with them to your own cultural level. I'm not saying 'Be Britain'; I'm saying allow yourselves to shape your own destiny.
What you have right now is a powerful gun lobby hiding behind an outmoded amendment that has no relevance to the modern world, meaning an issue is impacting your culture and you have no power to react as a society to it. It's the same as refusing to outlaw slavery because someone wrote down that it was fine 200 years ago - you have to be able to react as a modern country to the realities of the day.