The biggest attraction of doing it like that is based on the fact that at a minimum, you are looking at 6 months between time of purchase and actually receiving your firearm because of waiting on the ATF and a LEO. Now I'd be shocked if it is under a year with how busy ATF has been. This is specifically aimed at Class III and destructive items. And even after all that, if it's class III it still requires the tax stamp which means the ATF knows damn well who has what and where.
Again, how many crimes are being committed by this group? If this was the source of the gun violence problem, it would be worth looking at. But as it stands right now, its a legal method through which people with cash to burn can participate in a hobby and spend an absurd amount of money on ammunition because of how fast they burn through it. I'm sure the local gunshops/academy/walmart/etc love how much money these guys spend!
As for the site you linked, the lawyer is specifically talking about situations in which a LEO refuses to sign (they don't have an obligation to do it, they can leave it on their desk as long as they like). The lawyer is not calling out the weakness of the system, he is pointing out the ATF intimidating officers, which he gives a good example of if you follow the links he posted.
Not even sure why this is an issue.