William Barr is just the latest, and most dangerous, advocate of the unitary executive theory. From a legal and historical perspective, does it hold water?
No, because it ignores the role of Congress in the workings of the executive branch. The federal government is funded by a budget that is approved by Congress. Many executive officials are subject to the approval of the Senate. Finally, and most importantly, the organization of the federal government as a whole was established through legislation. Can you seriously argue that the president is, essentially, a king within his own branch of government when it is subject to all of those checks by the legislature?
In addition to the text of the Constitution, we know perfectly well that the Founding Fathers were influenced by the experience of the English Whigs in the 17th and 18th centuries. They knew about the Stuarts and their abuses of the legal system, and they would have been united in their desire to prevent them from occurring here. Jefferson and Hamilton would have agreed on this point.
If there is no basis either in the text of the Constitution or in the experience of the Founding Fathers for the theory, the only way it can be defended is by saying that Trump won a nationwide election and is therefore sovereign. He undoubtedly believes that; it is up to us to prove otherwise.