We treat independent agencies differently for many reasons, but Nina Mendelson of Michigan Law points to one more reason:
Several scholars, most recently and extensively Kevin Stack of Vanderbilt, have argued that statutes authorizing action by the “Secretary” or “Administrator,” without mention of the President, are properly read to deprive the President of directive authority over those executive officials’ decisions. Some have argued that reading delegations to a “Secretary or “Administrator” to authorize direction by the President would detrimentally affect an agency official’s willingness to resist presidential pressure, even though it would not affect the President’s formal power to remove the official. This short symposium essay responds by presenting more detailed evidence on several aspects of the interpretive question. It argues, consistently with the 2001 position of then-professor, now Justice, Elena Kagan, that outside of independent agencies, the choice of terminology does not communicate any particular congressional intent regarding presidential directive authority, at least with respect to executive branch agencies. Instead, a statutory delegation to the President, rather than to a “Secretary” or “Administrator,” seems best understood as Congress conveying the power to the President to choose which executive branch official will be primarily responsible for implementing that delegation, and delegations to the “Secretary” or “Administrator” as restricting that choice. The essay then comments that the interpretive question may not make that much difference to agency resistance to presidential supervision. It concludes with some observations on the normative debate over presidential control of executive agency decision making and calls for greater disclosure of the content of that control. (emphasis added)
A fine point or otherwise, collecting reasons for calling agencies “independent” tells us something about how governments decide to “bind their own hands”.