Oh, I agree. I also like the idea of an easily-accessible background system as the only measure on that front. I just don't think that's going to be enough given the emotional groundswell and the efforts of gun control groups to steer the legislation to prevention and not tracking.
The issue is that you've only settled one facet of the transaction. Yes, people can perform the checks but you have no idea if they are actually doing so. You will have no idea that a background check wasn't performed for a transfer until someone who shouldn't have the weapon uses it in a criminal act. There is no prevention in the system, merely a punitive aspect. Which is the way we work in America (and rightfully so) but, again, in the current cultural environment I think there is going to be a big call to be preventative.
In order to be preventative and for the government to ensure that you are following the rules, you'd need to present something like a bill of transfer along with a background check receipt. This would be reviewed and someone from ATF (or whichever entity inherits it) would follow up if the paperwork is out of order. This will be deemed necessary because to do otherwise would mean you support mass shooters in schools.