And so what if it is a "machine gun"? We should be able to buy those too.
Hand held machine guns are highly overrated.
However, the Second Amendment does not contain a rate-of-fire exception to the right to keep and bear arms. There are cases in progress right now wherein the lower courts have ruled "that arms particularly suited to military use are not protected". That is entirely nonsense.
Neither the Heller decision nor the Bruen decision overturned the 1939 Miller decision. Lower courts have lied about the Miller decision for nearly a century and anti-gun Supreme Courts have permitted it. Now it is possible that the Trump Court will recognize that Miller would have been exonerated if his prosecutors had failed to demonstrate that there is no military utility to use of a short-barreled shotgun. That would have been impossible since short-barreled shotguns, known as "trench guns", had been used in World War I.
The Miller decision rejected the notion that Miller needed to be a member of a Militia in order to receive Second Amendment protection. The Miller Court noted that they were not provided evidence that short-barreled shotguns were useful to a Militia. For that reason alone, the Miller Court remanded the case back to the District Court.
Miller either died or his lawyers failed to pursue the case (I can't remember which) and the Supreme Court decision was never acted upon.