You can make them illegal, but you can't make them harder to get.

To protect yourself from other gun owners, yes that's exactly right.

Also, the kind of people who'd buy an illegal firearm are exactly the kind of people we don't want to be armed.

Generally rational? It might be true there in the U.S. (though I doubt it), but here in Brazil, criminals will shoot you for any reason whatsoever, even if you don't react.

I'm from Brazil, and here gun possession is extremely regulated, meaning only a handful few people can own one.