I believe that the sole basis for the idea that the president has any independent powers at all aside from the veto and the pardon power derives from the opening statement of Art II, “The executive power shall be vested in a president of the United States.” That general statement is thought to somehow mean that the president has the power to do whatever he wants that isn’t formally legislative or judicial. In practice, he actually does get to nullify legislation and court orders, but we’re cool with that as long as he calls what he’s doing an “Executive Order”.
Clearly, the executive power of the US must include the power to order people to do things, right? So what’s your problem with the holder of the executive power ordering his people to do things that mere courts and legislators have forbidden? Let them go back to writing laws and opinions. Issuing orders to people is part of the executive power.