Au contraire. He/she most certainly could do that. Nobody can force a President to execute a law he/she considers unconstitutional. A president can proclaim a law unconstitutional and refuse to give it any effect. The only recourse is impeachment, which isn't going to happen if most people agree with the President's substantive position. Youngstown Sheet and Tube isn't on point at all. Even it it were, it's just a court case. Court's are powerless to give their decrees any effect. If the President can convince most voters that his view of the Constitution is correct, he/she can act in accord with that view and there is nothing anyone can do about it.
As a Clintonista once observed, “stroke of the pen, law of the land — Kinda cool.”
Well, using your application of logic, a President could do anything they wish, so long as they had the political capital to spend. That argument becomes, fairly quickly, absurd, especially in practical application.
"Youngstown Sheet and Tube isn't on point at all. "
Sure it is. Presidents don't have the authority to make law, and they certainly don't have the authority to ignore law, or so held the court in Youngstown. Presidents, using an Executive Order, can wield power that has been previously ceded to them by Congress and codified in statutory law.
"Even it it were, it's just a court case."
So was Marbury v. Madison. How did that turn out?
In the 230+ years of the Republic, when the Supreme Court speaks, the country listens, including the President.