Mexico isn't the usa. Every state that does have a conceal carry law, in which you are fingerprinted and registered, violent crime drops significantly.
No one is trying to find a perfect system. It's impossible. Background checks do however keep legally purchased-or purchasable firearms out of the wrong hands. Can criminals still find access, sure, but it beats just handing them guns at a gun store because they have cash. Over 2 million people have been denied firearms because of past criminal activity, that without the check, would have been able to purchase one as if it were say a bottle of shampoo.
The problem is not every sale requires one, there is no database for the laws we do have so no real way for a check to even be thorough enough to matter.
My favorite theory is this will only affect law abiding citizens. Because criminals won't subject themselves to a check. Well, if anyone has this mindset, I wanna point out that every single written law only affects the law abiding citizens. There's a "do not kill" law that criminals don't seem to be following, does that mean we should just take it off the books? No, laws don't affect criminals, but the penalties do. Let's re-examine our laws and penalties, plug the holes, solidify the system.
How about Illinois? I was under the impression they are like NYC and DC no handgun permits issued....