The constitution also explicitly sets up formal departments with specific purviews, with heads that need to be approved by congress. It also outlines that the president has the right to get the opinion of said principal offices about their duties (while seemingly failing to state any right to direct said opinions) This implies that the president’s executive authority over the departments is far from absolute, since if it was, why would you need to explicitly bestow a right to merely seek opinions?

If anything, the constitution implies that department heads SHOULD have independent opinions related to the purview of their departments.

“The President shall be Commander in Chief of the Army and Navy of the United States, and of the Militia of the several States, when called into the actual Service of the United States; he may require the Opinion, in writing, of the principal Officer in each of the executive Departments, upon any Subject relating to the Duties of their respective Offices, and he shall have Power to grant Reprieves and Pardons for Offences against the United States, except in Cases of Impeachment.”