You left out "general welfare." Exercises of police power that don't serve to advance of the public health, safety or general welfare are inherently unconstitutional. Your (deliberate?) omission of the general welfare is a very significant one, as this is the reasoning the Supreme Court has used to support local land use controls, including zoning, development standards, and quite specifically, historic preservation.
But I think I can see the problem here now. Some seem to be convinced that I'm trying to prove something here. I'm not. It just happens that I've been doing this exact thing for nearly 30 years. So I understand the law, local government rights and responsibilities under the law (especially in California), and how these determinations are made. I am simply attempting to impart information to those who might be interested in knowing more about how this works.
I'm not the least bit interested in debating the value of historic preservation in general, or the historical value of any given house specifically. If someone believes in their heart of hearts that historic preservation is not a worthy value for their own community to pursue, then fine -- petition your local government officials to not require the preservation of any historic buildings, and see how far you get. But please don't try to advance the argument that local governments don't have the authority to legislate historic preservation, or that they aren't required (in California, at least) to consider the impacts of their decisions historic buildings, or that determinations of historical significance are inherently arbitrary. All of these ideas are completely false.