Well, he was "only" the guy, who was writing down the items, as they were discussed during the convention. Surely, he had some insights. Maybe, you — in the 21st century — know more about the intent of those ancient legislators, but you aren't sharing... You just flatly say "wrong" — like a good little tyrant you secretly wish to be... Sigh, as they say, Statists gonna state.
Other founding fathers such as Hamilton understood the General Welfare provision very broadly.
Some citations would be useful here... As well as arguments for why we should be taking Hamilton's opinion over that of Madison and Jefferson.
But, if he was really so good, why are you proposing we "cherry-pick" Hamilton's ideas — instead of also electing the top executive ("national governor") for life — and have him appoint state governors?
I, for one, dread the thought of how this country would've looked, had that sort of tyranny prevailed — Russia, where the presudent's tenure is de-facto life-long and where he is appointing local governments even de-jure, is a very close example, actually.
Moreover, I suspect, you would've hated it too — had you even known about the man, whose opinion on "General Welfare" you advocate. You are wrong — the interpretation of "General Welfare" pushed by the Statists opens up a whole to drive a freight-train through. This was, of course, obvious for centuries. For example, that same Madison said later (1794):
The government of the United States is a definite government, confined to specified objects...If Congress can do whatever in their discretion can be done by money, and will promote the general welfare, the government is no longer a limited one possessing enumerated powers but an indefinite one..."
Indeed, whether it is to ban speech, confiscate guns, perform warrantless searches, seize funds and property without trials, eavesdrop on citizens' communications — the government would simply need to claim, those are done "for General Welfare". It would be a dreadfully depressing country to live in... Oh, wait...