No, the Fourth Amendment reinforces the principle that a citizen should be secure in his home against unreasonable seizure. If the government can control the party to whom you make a home sale, they have effectively seized control of your property.
I believe that’s the pivot on which the article turns. The author could have done a better job of laying that out, for sure.
Well if that’s the argument, the author is wrong about which Constitutional argument covers this. That’s a 5th Amendment Takings Clause argument, not a 4th Amendment search and seizure argument. That doesn’t mean I disagree with the substantive concern about the Federal Government rationing land use in a Soviet-style state controlled system. But the actual argument made is not Constitutionally correct.