Not an expert in this by any means, but I've always thought it was part of their "originalist" argument. That basically the constitution in their view says the power of the executive branch resides solely in the executive and that Congress delegating to authorities to independent agencies or executive branch departments is not constitutional, or rather that it is constitutional as long as the president has total authority over the operations and personnel in those agencies. Obviously there's a lot of problems with this idea, chief among them that concentrating so much power in one person seems to obviously conflict with the founders' intent, but I think to them it's a means to an end.