Sadly, we only have the GCA and NFA to thank for that. It's doubly bitter when you consider that binary triggers are legal (for now). Not exactly "full auto" proper, but close enough.
I was on another forum and we were talking about the GCA and NFA, and we actually had a chance in 1939 to toss it out in the Miller vs United States case (307 U.S. 174, 59 S.Ct. 816, 83 L.Ed. 1206 (U.S.Ark. 1939) when two men were charged with transferring a double barrel 12-gauge shotgun in violation of the NFA. A federal district court quashed the indictment, ruling that the NFA did indeed violate the Second Amendment. But the Supreme Court, in a unanimous decision, disagreed. Justice James McReynolds dismissed the case with the statement "the absence of any evidence tending to show that possession or use of a 'shotgun having a barrel of less than eighteen inches in length' at this time has some reasonable relationship to the preservation or efficiency of a well regulated militia, we cannot say that the Second Amendment guarantees the right to keep and bear such an instrument." McReynolds added that "certainly it is not within Judicial Notice that this weapon is any part of the ordinary military equipment or that its use could contribute to the common defense." He also noted that many states had adopted gun-control laws over the years.
The funny thing is, that statement and logic, today, actually supports the removal of at least short barreled rifles, short barreled shotguns, suppressors and machine guns from the NFA list as all are absolutely "a part of the ordinary military equipment." Unfortunately, I don't see that happening.
It's also a bit ironic that in many European countries, where guns are much more restricted, the purchase of suppressors are not. Heck, they don't even put serial numbers on them.