True that FHFA and CFPB have an at-will Director terminable only by POTUS, and both have non-appropriated funding.
But whereas CFPB has no oversight board, FHFA *does have* a 4-member oversight board with broad power, that must convene quarterly, and must “testify” annually to Congress, whom can then give feedback. This is the Federal Housing Finance Oversight Board (“FHFOB”).
This distinction is not a clear cut game-changer, but if I am the USA I appeal to Chief Roberts’ idea positive structural checks (see Bowsher v Synar, and Seila v CFPB): FHFOB is a legislated check on material operational misfeasance. And issues of funding are clearly operational issues. So despite the curiosity of one Agency (FHFA) collecting all revenue from a few very large regulated GSEs, Congress did not fully divest itself of its funding power because the FHFOB is its effectively its eyes and ears.
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