First, the decision of Train v City of New York may not be analogous to your FEC example. A pivotal fact in Train v NYC was the statutory language left no discretion with the President to decide how much money was to be disbursed. I’m not sure the FEC statute has similar language leaving the President with no discretion concerning appointments (maybe it does, I haven’t yet looked.) Regardless, the FEC is not a “legal nullity.”
The operative word, of course, is "analogous". I don't disagree that the statute in Train was specific, but the concept is certainly the same. Hence, "analogous." Additionally, the appointment provisions of the FEC statute are quite specific, and the agency is intended to be an independent regulatory body (for this very reason). As such, the statute specifies that "no more than three Commissioners can represent the same political party, and at least four votes are required for any official Commission action. This structure was created to encourage nonpartisan decisions."
FEC Leadership and Structure. The statute is available
here. The point, really, is that by keeping the Commission under a quorum it is effectively unmade, although the agency continues to exist.
52 U.S.C. §30106 (c): Voting requirements; delegation of authorities
All decisions of the Commission with respect to the exercise of its duties and powers under the provisions of this Act shall be made by a majority vote of the members of the Commission. A member of the Commission may not delegate to any person his or her vote or any decisionmaking authority or duty vested in the Commission by the provisions of this Act, except that the affirmative vote of 4 members of the Commission shall be required in order for the Commission to take any action in accordance with paragraph (6), (7), (8), or (9) of section 30107(a) of this title or with chapter 95 or chapter 96 of title 26.
Those cited provisions include: (6) to initiate (through civil actions for injunctive, declaratory, or other appropriate relief), defend (in the case of any civil action brought under section 30109(a)(8) of this title) or appeal any civil action in the name of the Commission to enforce the provisions of this Act and chapter 95 and chapter 96 of title 26, through its general counsel;
(7) to render advisory opinions under section 30108 of this title;
(8) to develop such prescribed forms and to make, amend, and repeal such rules, pursuant to the provisions of chapter 5 of title 5, as are necessary to carry out the provisions of this Act and chapter 95 and chapter 96 of title 26; and
(9)
to conduct investigations and hearings expeditiously, to encourage voluntary compliance, and
to report apparent violations to the appropriate law enforcement authorities.
And failure to “faithfully execute” a statute is not, per se, an impeachable offense. Trump, refusing to enforce 40 U.S.C. §8103(b)(2) against a person who “willfully” injured several “shrubs” by purposefully mowing over them. Now, you may argue the potential harms aren’t the same where the potential harm from a non-functional FEC is different than the shrub statute. Fine. But the harm shouldn’t be presumed to exist, the harm needs to be palpable, and shown to be worthy of impeachment.
Again, I don't disagree. In this instance, however, that harm is clearly "palpable and clearly shown to be worthy of impeachment." Presumption is not required, it is provable (see, conviction of Michael Cohen). This is part of a pattern by this President, as noted earlier (consider the entire Department of Homeland Security) but in the
particular circumstance of the FEC is being undertaken to protect the President himself from investigation and potential impeachment and prosecution. (By the way, if the President had "willfully" injured several "shrubs" in violation of a statute, he could, legitimately, be impeached for that, if it was determined that his willful behavior was detrimental to the nation and beyond his constitutional authority. High Crimes and Misdemeanors incorporates the higher standard
expected of the Chief Executive. If that behavior would be deemed adequately detrimental, goodbye Mr. Chips.)