If your question is whether the “independent” agencies are Constitutional, the answer is yes. Congress makes the laws and the laws can constrain the behavior of the President. If the law says the President cannot fire someone, or interfere in an agency’s work, then the President cannot.
So who are such agencies accountable to? Congress. Just like the president is accountable to Congress.
So who are such agencies accountable to? Congress. Just like the president is accountable to Congress.