Without the Dept. of Education, HUD, the National Endowment for the Arts, National Public Radio, Medicare, Medicaid, Social Security, foreign aid, often ill-conceived involvement in foreign wars and other affairs, etc, etc. ad infinitem and ad nauseum.....
Don't forget the EPA. Definately not within the realm of Federal authority as far as I can see.
I'm not sure I agree with you on the Foreign Aid, that may fall under the ability to enter into treaties.
As for the "often ill-conceived involvement in foreign wars"...
Section 8, Clause 11: "To declare War, grant Letters of Marque and Reprisal, and make Rules concerning Captures on Land and Water;"
They may be ill-conceived and foolish wars, but they have the power to declare them.