The "Universal" argument is that you cannot sell Fred, your well known shooting buddy at the gun range one of your rifles without checking his status.
Now, truth be told it also means you can't sell Teddy, who answered your Craig's List ad, a gun either. But you don't really know Teddy.
In all seriousness, I'm not going to sell anything to someone I don't know reasonably well anyway. And for that matter neither is any one lose I know.
But a stolen goods fence is going to sell it to whoever will give him cash for it.
So the reality is that this will have exactly zero effect on illegal gun traffic, or at lest minimal effect. But it will provide the "original hooks" for a nation wide registration system.
As I mentioned earlier, anyone who really still believes that their Social Security number isn't an ID number is a moron. But in the beginning it was loudly proclaimed that it wasn't and couldn't ever be used as a national identification system. So what do you put on your 4473 and your 1040? This very same "non-identification" number.