It's a fair question to ask "who are independent executive agency heads accountable to" in a constitutional context. It is true that the Executive Branch has grown far beyond what the Founding Fathers could have imagined, but the idea of a unitary executive is that the President is responsible and accountable for everything that happens in the Executive Branch. If the voters don't like what the Executive Branch is doing, they can replace the President in the next election. What happens if voters don't like what independent executive agencies are doing? There's no democratic recourse.
Think of a scenario where a President was elected with a large-ish majority and promised during the campaign to change broadband regulations to reduce broadband prices across the country. Unfortunately, the FCC commissioners were all appointed by the previous president and block this policy change that the voters clearly support. How does that square with democratic accountability?
The problem is that Congress has delegated a lot of its traditional law making power to the Executive Branch. Laws are written in vague ways with executive agencies given liberty to implement as they see fit. This gives a lot of additional power to the President (who can at least be dealt with by impeachment or being voted out in the next election) as well as independent executive agency heads (who can't be directly fired by anybody). I agree that Congress should be the ones passing laws as the excessive delegation of lawmaking by Congress is what's gotten us into the current situation
none of the authority Congress has delegated has been delegated irrevocably. if you want to change how the head of the FCC is appointed there's this thing called a law that can't be passed to change it
Think of a scenario where a President was elected with a large-ish majority and promised during the campaign to change broadband regulations to reduce broadband prices across the country. Unfortunately, the FCC commissioners were all appointed by the previous president and block this policy change that the voters clearly support. How does that square with democratic accountability?