If the 25th amendment is not activated under these circumstances, it may as well not have been...

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9. Part of the analysis is that it's markedly harder than impeachment

You need the vice-president *and* a majority of the cabinet *and* 2/3rds of the House *and* 2/3rds of the senate.

That's a tall order, and deliberately so. It was intended for situations where it was widely agreed, even by most of his trusted cabinet, that he was unfit for office.

Yes, it's possible that some president could have a mental illness, be widely recognized as unable to perform the duties of office, even according to his cabinet, and not have committed any impeachable offenses (which includes neglect of office or critical duties, e.g.), in which case removal by the 25th amendment could happen.

But it's very unlikely, if only for the practical reason that impeachment is so much easier. If you had support for removal via the 25th, you surely had support for removal by impeachment before it got to that stage.