The article is confusing a few different things and in the course misunderstanding the structure of the US government.
For example, you really can't talk about independent agencies in the same way as normal executive branch agencies. One is under presidential control and the other isn't, by definition.
But the big thing I'd respond with is this: the reason the US has a president in charge of the executive branch is because then he can be held to account for executive branch functioning.
If the president wants to fully own the DOJ, then great! He will personally stand for impeachment should the DOJ misbehave.
That's the trade.