1. If it is not a crime then why the referral to the Police?
Because it is suggestive that a crime has been committed. It's not a crime to be in the same room with someone shouting "Help, help, call the police, I'm being murdered." But such calls will usually result in a referral to law enforcement for investigation. If there was, in fact, no murder, then you haven't committed a crime, notwithstanding the referral.
Since the 4473 is a Federal Government form and approval must be given by the Federal Government why would local Police be notified as they have no authority in Federal Law
Setting aside frequent overlap in state law prohibitions, I think you are incorrect that local law enforcement has no ability to investigate federal crimes. They are not obligated to do so, but they can investigate and cooperate.
Hoping the Police will show restraint is a very thin thread to hang onto.
This is a legitimate concern, as I think I have plainly acknowledged in prior posts.
Sorting out the disposition of a criminal charge can be very difficult.
As someone who has frequent professional occasion to deal with court clerks, I have no doubt that this can be somewhat challenging at times. The difficulty pales in comparison to many other tasks that we (perhaps unreasonably) thrust onto law enforcement agencies.
On the larger topic, if the NCIS system is as thoroughly a joke as you contend (and you may be correct), then perhaps bringing its absurd failures and unreliability to the fore is the best course of action. Perhaps it would take some of the steam out of the eternal cry to have "universal background checks" for every firearm transfer.
I'm reminded of the episode (perhaps a repeated one) wherein a new sheriff was elected in a dry (no-booze) county. Not a fan of hypocrisy, he promptly raided the country club where the other county authorities were enjoying a boozy, happy, and illegal cocktail hour. Within a month, the county went wet. Which suited that sheriff just fine, as he no longer had to waste time arresting the plebes for their six packs of cheap beer.