The Supreme Court has described the major questions doctrine in different ways, but here is one formulation, taken from Util. Air Regul. Grp. v. EPA, 573 U.S. 302, 324 (2014):
When an agency claims to discover in a long-extant statute an unheralded power to regulate ‘a significant portion of the American economy,’ [the Supreme Court] typically greet[s] its announcement with a measure of skepticism. [The Court] expect[s] Congress to speak clearly if it wishes to assign to an agency decisions of vast ‘economic and political significance
Shutting down the CFPB is obviously of vast economic and political significance; conservatives have consistently described the Bureau as exercising vast power. The power to shut it down, or in Elon Musk’s words, CFPB RIP, is unheralded. The CFPB’s organic statute, enacted in 2010, is not “a long-extant statute,” but plenty of other statutes have created agencies and I’m not aware of any agencies Congress created that the executive branch later shut down–until this year. So it looks like we need a clear statement that the CFPB can shut itself down–and we don’t have it. And don’t be fooled: leaving the CFPB alive only to assist in setting mortgage rates is shutting it down, or as close to as makes no difference.
