Not all guns could be eliminated, because it was in the 50s (i think) when guns were banned.
Just to let you know:
There are no gun manufacturers in Mexico, if you want to get a gun by your own, you must buy one in USA, then attempt to cross the border with it (very risky). If you don't dare to get it on your own and decide to buy it illegaly, you will have to go and deal with criminals, that will sell the gun at a very high price.
Let's say that there are around 10,000 weapons in Mexico, all of them illegal, if the goverment decided to make guns legal, the number will increase from 10,000 to 10,000,000 in a very short time, what does this do?, it will only give criminals an easiest way to get guns to commit their crimes.
So you are one of those that think that drugs should be legal, since their current illegal status doesn't avoid people from being addicted to them. See what i mean?, if they make drugs legal, the number of addicts will increase, just because everybody will be able to get LEGAL cocaine in the drug store. The same goes for guns.