So by your logic, the welfare clause and the commerce clause (which, yes, have been abuse to the nth degree) would pretty much cover anything. If that's true, then what, pray tell, would be the purpose of the 9th and 10th amendments? Seriously, if the founders indeed intended for the feds to do pretty much whatever, then why specifically spell out that "all else is the purview of the states and the people"? There would be no "all else". Makes no sense.
Of course the writings of chief architects of the Constitution (Madison, etc. in the [anti]Federalist Papers, etc) made it quite clear what their intentions were with respect to this debate.
But you are right, there was a debate even among the founders, with Madison and Jefferson on one side, and Hamilton on the other. And yes, things went off-kilter pretty much right away. The Constitution is by far a perfect document, as it was a compromise between the two camps. But compared to where we are now (rather close to collapse) I'd much rather be back at the point of that awful compromise.