Congress does regulate those weapons.
There's a reason you can't just walk into a Wal-Mart and walk out with a machine gun, or a rocket launcher.
That said, I don't much care for the fact that the requirement to have legal access to machine guns is "be rich enough to buy your way around the law".
Personally, I do think we need a complete re-work of the way we treat weapons to reflect the realities of the modern world.
(1) We have four hundred million weapons in the United States. It is horribly negligent that safe weapon handling is not taught in schools, at multiple levels. Also a good touchpoint to get police interacting positively with the community.
(2) The current background check system should be replaced with a Swiss-style one; e.g., you get a code, valid for say a week or two, that any seller can use to verify that you have passed a background check.
This doesn't create a de-facto registry, so no problem getting gun owners (or the NRA) to go for this one.
(4) A red-flag law that allows immediate family members and healthcare professionals to temporarily bar an individual from purchasing weapons, with safeguards in-place to keep bad actors from abusing the system (e.g., a psychiatrist that just reports all of his patients to the system because he opposes gun ownership).
(5) Removing gun rights only in the case of violent crime. Right now, in most states, misdemeanor assault won't cost you your gun rights, but a felony for tax evasion will. That's ass-backwards.
(6) Machine guns, grenades, rocket launchers, and the like should be available with a license. You really need to be able to show that you can handle these things safely. Right now, it's just "be rich".
(7) Treat short-barreled rifles and shotguns as normal firearms, and silencers like any other accessory.
(8) Concealed-carry should be the same for police as it is for normal citizens. Same licensing requirements: a one-day course, including a test on safe weapon handling. This also ends gun-free zones: if you have a license, you can carry wherever you want.
(9) Open carry needs to work differently for urban and rural areas. The above permit will allow you to open-carry a pistol in an urban area. Rifles, no. Put it in a case. In the countryside, open carry just makes sense.
(10) Actually prosecute straw sellers. Buy a gun for somebody that can't legally buy one on their own, you permanently lose your gun rights, plus whatever punishment makes sense.
(11) Secure storage requirements. If one of your weapons is stolen and used for a crime, you are legally an accessory if you can not demonstrate that you took reasonable measures to store the weapon securely (e.g., a gun safe or lockable case). This doesn't require police inspections, but provides a strong incentive for personal responsibility.
All of this would enjoy massive support from gun owners, and address a lot of existing problems.