The idea that Congress can set up agencies that are outside the control of the Executive needs to be revisited. It leads to rogue, unaccountable bureaucracy.
The point was to eliminate the concept of a king. The president was meant as a figurehead, with almost no power.
There is a reason the US has three branches of government instead of one despite misguided individuals that believe otherwise.
Whether they are “co-equal” depends on who you ask but it is a lie to claim they are not accountable when their accountability is to congress directly via funding.