Your point is moot. They are allowed by the law to benefit "the agency" ie the tax payer
(a) The Recovery Act grants the FHFA expansive authority in its
role as a conservator and permits the Agency to act in what it determines is “in the best interests of the regulated entity or the Agency.”
§4617(b)(2)(J)(ii) (emphasis added). So when the FHFA acts as a conservator, it may aim to rehabilitate the regulated entity in a way that,
while not in the best interests of the regulated entity, is beneficial to
the Agency and, by extension, the public it serves. This feature of an
FHFA conservatorship is fatal to the shareholders’ statutory claim.