It doesn't have to. The Commerce Clause gives the government the authority to regulate. When it has the authority the regulation takes place regardless of whether there is commerce in individual cases.
Yes. The best example of Commerce Clause authority is found in Wickard v. Filburn, a case from the Depression era where FDR's Department of Agriculture took action against a farmer who grew 11 acres more wheat than he was allocated to grow under FDR's Agricultural Adjustment Act. This Act gave FDR the power to dictate how much wheat could be grown and marketed. It was part of FDR's deliberate suppression of food production during the Depression in order to create artificial shortages in order to keep prices up, which FDR thought would help the economy recover (it didn't). Filburn's 11 acres of excess wheat were grown and used on his farm, to feed his family and his livestock, none of which ever entered commerce at all. The Court (a very Progressive one) ruled that because Filburn grew wheat that he was forbidden to grow he did not have to buy wheat in the government-controlled marketplace. This, the Court concluded, if done by many people, would "affect" interstate commerce in wheat by reducing demand and thereby interfering with FDR's desire to control the market for wheat.
Other Court precedents have upheld the notion that if an objects, or any part of an object, or in some cases the raw materials that object is made from ever enter "interstate commerce" by either physically crossing a state line or by "affecting" interstate commerce in literally any way, Congress can regulate that object even if the object itself never crosses a state line or is never used in "commerce" and is only used by a private individual.
The effect of these Progressive-era rulings is that there is almost nothing that Congress cannot regulate because nearly everything will in some way or another "affect" interstate commerce according to the Wickard v. Filburn rationale.
In the last decade the Supreme Court has made a few minor adjustments to this near-plenary power of Congress to interfere with the lives of individuals using the Commerce Clause power. The most pertinent is gun related. The Court threw out a law that prohibited the possession of firearms within 1000 feet of a school by ruling that the justification for invoking Commerce Clause authority to make such a law was that schoolchildren eventually grow up to be workers who may move between states and therefore the federal government had authority to regulate gun possession near schools in order to protect these nascent workers in "interstate commerce." The court, after decades of deferring to this sort of assertion on the part of the government finally held that the alleged link to interstate commerce was too tenuous and that if upheld would grant the Congress virtually unlimited power to regulate every aspect of our lives, which defies the very concept of limited government enshrined in the Constitution.
It was a small but important victory.
But it still remains true that if the device or service ever enters interstate commerce, Congress can regulate it as it sees fit. The purpose of the "permission slip" for NFA items is to discourage interstate "commerce" in NFA articles by tightly regulating their possession, transfer and transport. This was done because at the time the GCA was passed the use of machine guns other NFA items was allegedly problematic for the federal government during the Gangster Era. It's probably an entirely unnecessary regulation now, but government agencies are loathe to give up power and control once they have it.
But, in point of fact that's exactly what happened with regard to suppressors. The BATFE has exempted suppressors from the requirement to obtain prior permission to transport them across state lines, although this does nothing to guard against state prosecution if you transport it into a state where suppressors are unlawful, and they specifically say this in the manual. In theory, the Volkmer-McClure Act, which guarantees the right to transport firearms through states where it is unlawful to possess them, including stopping enroute, so long as your destination is to a place where the firearm is lawful, and this ought to apply to suppressors as well, as they are classified as "firearms" in the law.
However, some states, New Jersey and New York being notable among them, often ignore Volkmer-McClure and routinely arrest people traveling through their states in possession of "illegal" weapons (like any handgun that can hold more than 7 rounds), and seizing (permanently) the "illegal" firearms.
So the upshot is that you do not have to file the form to transport a suppressor interstate, but you still need to comply with state laws and be careful when transporting them so as not to get them seized by some overzealous cop.
