>> As the legislative history of the law discloses, its underlying purpose was to curtail, if not prohibit, transactions in NFA firearms. Congress found these firearms to pose a significant crime problem because of their frequent use in crime, particularly the gangland crimes of that era such as the St. Valentine’s Day Massacre.
>> United States v. Freed, 401 U.S. 601 (1971), was a United States Supreme Court case in which the Court held the National Firearms Act's registration requirements do not violate the Fifth Amendment of the United States Constitution.
https://www.atf.gov/rules-and-regulations/national-firearms-...
Also, the supreme court already weighted on some rights regarding weapon registration:
https://en.wikipedia.org/wiki/United_States_v._Freed
>> United States v. Freed, 401 U.S. 601 (1971), was a United States Supreme Court case in which the Court held the National Firearms Act's registration requirements do not violate the Fifth Amendment of the United States Constitution.