In the context of the US, what right would, in theory, prevent a national law that regulates or prohibits the capture of biometric information of people while o

In the context of the US, what right would, in theory, prevent a national law that regulates or prohibits the capture of biometric information of people while out in public? There is a common quip that some rely on that "there is no expectation of privacy while in public", but that's an aspirational statement rather than a strictly legal one. Setting aside government mass surveillance for the moment, could the US regulate private mass surveillance that records people's identifiable biometrics?