All legislative Powers herein granted shall be vested in a Congress of the United States, which shall consist of a Senate and House of Representatives.
Anything short of "all" contradicts that.
Now you need to find somewhere that says "Oh, btw.. we didn't mean 'All' but really 'some' because Congress might give some legislative powers to other branches."
This “anything not expressly allowed must be forbidden” is the exact opposite of how US law works.
With regards to the Constitution, the 10th Amendment would disagree.
Congress would have to vote on giving approval for each new drug, not the FDA's bureaucrats.
Congress would have to vote on each individual edge case for welfare programs (SNAP, Social Security, Medicaid, etc), not their respective agencies.
Congress would have to vote on which individual people get Pell grants, how much, and how much their parents are expected to contribute to their university schooling, not the Department of Education.
Congress would have to vote to approve contracts for every federal agency.
The federal government would not function without some degree of delegation.
You don't change the law every time a new drug gets approved, you grant it certification (the framework of which is based in existing legislation). You'd only need Congress to get involved if you wanted to change the approval process itself