The Court did not say that the Takings Clause can be used to justify taking one house to replace it with one business. On the contrary, they relied on the overall plan and the benefits of a major redevelopment. Your position would permit direct transfers of one piece of property from one private owner to another based solely on a net benefit in General Welfare (such as higher taxes on a store than a house or farm). The Court rejected that logic.
You might want to consider reading the opinions.
First of all "Promote the General Welfare" is not in Article I, it is in the Preamble.
Secondly, if you want to get down to original intent in regard to the Bill of Rights, then the fifth amendement does not nor was it ever intended to apply to the states or local goverments. The Bill of Rights was intended as a reservation of rights for the citizens of the various states against the Federal Government and not from their own states.