That’s contrary to what the authors of the constitution have meant when they wrote it. See my other comment. Roughly speaking, if the “general welfare” was supposed to mean “anything the congress wants to do to provide for general welfare”, there would be absolutely no point in enumerating the powers it does have. Madison was extremely clear about that, and this is how this article was universally understood (otherwise, the constitution would have had no snowball chance in hell of passing) up until Helvering v. Davis, when it was promptly thrown away and replaced with the opposite of original intention.
While I sympathize with your argument, I have to point out that, considered as a general argument about why specific powers are enumerated in the Constitution, the first blow against it was struck long before Helvering v. Davis. In McCulloch v. Maryland in 1819, the same expansive logic that wasn't supposed to be used, according to Madison, was applied to the necessary and proper clause, in order to argue that a national bank was constitutional even though that specific power is nowhere enumerated.
In fact, you could argue that it goes back even further than that: in Marbury v. Madison in 1803, the Court ruled that it had the power to declare acts of Congress unconstitutional, even though the Constitution nowhere says the Supreme Court has that power. One could argue that that is implicit in "judicial power" (and that's basically what Chief Justice Marshall argued in his opinion), but the larger point is still valid, that way too many things were left unstated and implied in the Constitution for arguments like the one of Madison's that you refer to to work in the long run.
It's also worth pointing out that not all of the Framers agreed with the viewpoint Madison expressed that you refer to. Marshall, for example, was one of the ones on the other side: he thought rulings like the one he made in McCulloch v. Maryland were perfectly well within the intended meaning of the Constitution and were not expanding the intended Federal power at all.
