Look Federalist no. 41, which I've read before, was written by James Madison, not Alexander Hamilton. Hamilton himself disagreed with Madison's logic, and mocked it by quoting his statement elsewhere that "no axiom is more clearly established in law, or in reason, than that... wherever a general power to do a thing is given, every particular power necessary for doing it, is included" during his debates with Madison in congress, when Madison disagreed with Hamiltons attempt to justify the program given in his Report on Manufacturers through his broad interpretation of the general welfare clause. Madison's position is illogical - why would a clause that grants a general power somehow be limited to other more specific clauses mentioned elsewhere? Its redundant, why not just not include it, or specifically mention your ridiculous logic that it's somehow only an utterly pointless reiteration of what was said elsewhere?
The clause does not give the government every power imaginable for the "general welfare", it is confined to the realm of spending tax money due to its presence in the taxing and spending clause. So, for instance, the ban on marijuana derives from the regulation of interstate commerce, not the general welfare clause. Nor could the federal government say "Gay marriage is now legal everywhere, due to general welfare clause."