An important historical reason for accepting general powers was the belief by many courts that the legislature could not delegate the right to make rules to an agency.  While this has been rejected, it left early courts with the choice of requiring a specific law by the legislature on everything, which was impossible, or letting the agencies use general authority.

The United States Supreme Court has never limited the state's right to use general powers in public health unless those are a sham to evade other constitutional protections.[Yick Wo v. Hopkins, 118 U.S. 356 (1886) - regulations that applied different standards to Chinese owned laundries were stuck down]  Unless the legislature has passed laws limiting the health department's use of general powers, the state courts have generally not interfered with the use of general powers.  This is especially true for classic public health enforcement involving clear and immediate threats to health.

Many state legislatures have been successfully lobbied to limit the general powers of health departments, especially in communicable disease control.  These can make public health actions difficult, but can be changed since they are not constitutional limitations. Many provisions of the model emergency health powers act are just restoring powers health departments had before they were limited in the 1980s and 1990s.