One doesn't deserve such a huge reward from being fortunate enough to have a good idea and doing the nominal work to implement it. By granting them that, they unfairly benefit in contrast to the rest of society.
Besides, I think the O.P. meant for the discussion to be limited to whether gun control would bring gun violence down, and not open to the question of whether it would increase the likelihood of an oppressive gov't takeover and people's personal opinions on that.
The state has weapons decades beyond guns available to it. Guns will not provide an effective resistance to a population against an oppressive U.S. in possession of police and military weapons and gear.
This point doesn't rule out the premise (unless by "greatest" the premise-maker meant "harshest"). But even so, you can't say for sure which you would prefer (unless you've experienced them... which I'm hoping you haven't). Don't meant to play devil's advocate, it's simply true.
All? That's absurd. What about the problems caused by the other economic systems? Disease? Domestic abuse? This also depends on what you consider to be problems. Do you include personal problems faced by many (such as emotional trauma, health issues)? But mostly, this premise is ridiculous.