Machine guns are a Class 3 firearm, which does require a tax stamp. But obtaining the stamp takes about 20 minutes of work and 3-6 months of waiting for the ATF to do the paperwork and background check. They don't do a face-to-face background check like they do with a potential gun dealer, and you don't need an FFL to get a tax stamp; it's entirely online these days. They request a fingerprint card, but the gun stores typically do those on-site and mail it in for you along with any other paperwork. And the tax stamp costs a whooping $200, which is not a significant sum.
The only reason machine guns aren't more common is the fact that the registry was closed in 1986 and no new machine guns have been manufactured since. Thus, the cost of even the cheapest fully automatic firearm starts at $20,000, which is the true limiting factor. If there were still new machine guns to be had for a thousand dollars, everyone would have them, given how cheap and easy a tax stamp is to get.
The biggest problem with expanding the NFA is that, as understaffed as the ATF is, it would take a DECADE or more to add all the guns, during which time no new ones could be manufactured and sold, and anyone attempting to buy one afterwards would have to wait years for the ATF to complete the paperwork and get their stamp. And that alone would be enough for the Supreme Court to rule that gun owner's rights were infringed upon. So before the NFA could be expanded, you'd need to spend billions on expanding and streamlining the ATF.