“......Most of those powers are mandated by treaty.”
The Department of Education, the Department of Energy, the EPA, etc. were all caused by some need established by a treaty with some foreign entities!?
The powers they wield were, yes. The decision not to disband the DOE was an agreement between Reagan and Gorbachev as recounted in Charlotte Thompson Iserbyt's book the deliberate dumbing down of america. The legislation authorizing the powers of the EPA specifically cites multilateral treaties, particularly Section 1531 of the Endangered Species Act.
If you wish to understand how this all started, start here.