Banning firearms will not finish the problem, but will very likely decrease it.
I know that single-account experiences are not statistically important, but anyway, it's not the only time I have heard such an account — And all I know is what I (or my close ones) have lived.
My family in Argentina were robbed at home, at gunpoint. The robbers asked them to hand over (in this order) firearms, jewels and money.
If firearms are harder to come by, they will not be likely to be found in a regular person's home. Of course, the black market will still have them — But the black market will have higher prices for them. Fewer wrongdoers will be able to get their hands on weapons.
If you add to this programs such as one implemented in my city, where the local government asks you to (voluntarly) hand over any guns you have paying for them in more useful goods (such as a computer, or even cash), the amount of guns in the street decreases. That means, the amount of armed people decreases. And the price for individual guns (let alone "specialty" guns, which should just be banned outside of army use) goes up. Everybody wins.