It might be time to start thinking about the wording of the 25th Amendment, and the meaning of “unable to discharge the powers and duties of his office” in that text. It does not require illness of mental illness, it does not require “high crime and misdemeanors,” just inability, which is ultimately a subjective judgement. I have not reviewed the constitutional history, but surely this Supreme Court would be reluctant to read anything into the formal text that was not there.
Note that the process itself is triggered by the “Vice President and a majority of either the principal officers of the executive departments” sending a letter to Congress. You might think that that would help explain Trumps Cabinet appointments. But there is another possibility. The full text of that part of the sentence is ” Vice President and a majority of either the principal officers of the executive departments or of such other body as Congress may by law provide” (emphasis added.)
So, at least in theory, regardless of who is in the cabinet, Congress could change the description of the deciding group, by a veto proof majority, to whoever it saw fit. Then all that the triggering of the complex removal process would require would be the Vice President and a majority of that group (say living retired presidents). So the VP’s assent is key, but the cabinet’s might not be.
Quite a ride indeed!
P.S. (January 10, 2017) Richard Cohen, of the Washington Post, explores this approach here, and links it to the confirmation process.