You’re begging the question: What makes an agency “independent”? The answer given by the original poster was “because Congress says so, and they can”. That is, again, flatly wrong.

Congress can’t reorganize the Treasury as an independent agency. Why not? Making the sole director of the CFPB dismissible only for cause was ruled unconstitutional. Why?

Taking the claim made by the original poster as accurate would lead you to get both of these important questions wrong.