The Constitution makes clear that all executive power is invested in the president. https://constitutioncenter.org/the-constitution/articles/art.... It’s literally the first sentence of Article II.

So you can have a civil service (and the framers assumed there would be one) but Congress can’t insulate the civil service from the president’s direct supervision. That’s obviously true—because the presidential election is the only way people have to politically influence the internal operation of the executive branch itself.

I'm waiting for the unitary-executive crowd to admit that they're monarchists at heart — and not constitutional monarchists.