If it's so they're hardly independent agencies, and the point of this executive order is indeed to eliminate the independence.

No because "independent agency" just mean the agency was established by law, with a specific mandate and regulations that the President can't independently change.

It doesn't mean the agency isn't a part of the Executive branch with the President at it's head and it doesn't mean the President can't fire them for specific reasons.

Again, if the president can have a strong influence on them, they're not independent, however they might get called