Earlier quoted context omitted.
They aren't 'independent' they are 'a mix between executive and legislative'. The Supreme Court decisions are Meyers v US and Hunters Executor v US. And I'm not a constitutional scholar but my reading of it is that the protections in question come from the legislative delegating some of their power to the executive, think legislative actions (researching laws, etc) but retaining their constitutional prerogative to pr…
“ Myers v. United States, 272 U.S. 52 (1926), was a United States Supreme Court decision ruling that the President has the exclusive power to remove executive branch officials, and does not need the approval of the Senate or any other legislative body.”
It limits that power when it comes to the quasi-legislative agencies.
That was the unambiguous law of the land for nearly 100 years until the current court whittled down the exclusion in Seila in 2020.