The state governments were "subordinately useful" because ALL governments are supposed to be subordinately useful - in subordination to the sovereign people. The use of ill-defined terms is usually indicative of the sort of sloppy thinking that tends towards centrality in federalism. I've long noticed that, by "states", federalists can mean 'state governments', 'state territories', or 'people of a state' according to immediate argumentative need. "States" are 'the People' when ratifying the Constitution, but are not 'People' when it is, in short order, necessary to distinguish the states from the central entity which is now also/rather/instead/sometimes 'the People'. To believe that the adoption of the new constitution through the states is a genuine political expression of the People but that the same arrangement had previously thwarted the People's will is fatally contradictory. Either "the People" work through state governments, thereby both legitimizing the Constitution AND validating the system under the Articles, or else do not, which would both invalidate the old Confederation AND delegitimize the Constitution. The argument is self-eliminating.
That’s not the point Madison is making. It’s very clear what he was saying. He was saying that the new national government would be supreme in every significant and feasible way. He was saying it was “inexpedient” to try to eliminate state governments altogether, but it was no matter—they could leave the states with trifling duties. They would basically be subordinat administrators. And look around—that’s exactly what they are.