Like the president approving a congressional appropriation that cuts their departments by 10% or for disagreeing with his foreign policy say in the middle of a war?
It's being discussed yesterday and today as a loophole to work around Congress not doing impeachment and conviction. This is a legalized coup. Now most agree with the coup and the reasons, but it's still a coup. We have an established process for removing a federal official from office for cause-impeachment followed by conviction. The 25th Amendment is a cause-less removal, yet people want to use it de facto as a "for cause" removal.
This is an awful lot of power to give to a bunch of mostly unseen people that have never faced a ballot box. Once you break the glass once, you don't break the glass twice, you follow established precedent. I just feel the 25th should be clamped down so that the method and process to remove the president for cause remains with Congress and that the Cabinet act as mere reporters for the obvious medical cases. That this is even a thing and has now been brought up 2 times, it's less that this is something Cabinet should do and more because people want Congress to do something that Congress has shown itself unwilling to do.
By definition, utilizing the Section 4 of the 25th Amendment, it is not a legalized coup. A coup d'état has a specific definition, primarily that is is an illegal and/or violent overthrow of the government. Section 4 of the 25th Amendment establishes a legal procedure for stripping the President of his powers if he is deemed "unable to discharge the powers and duties of his office". You may argue for medical cases only, but mental ones are far more subjective and may be no less medical in nature. Even so, the 25th Amendment already contemplated the issue of a Vice President and Cabinet (or other body) voting against the President. It requires Congress, with a 2/3 vote of both Houses, to sustain the VP and Cabinet (or other body).
It's no more a coup than a non-confidence motion in a parliamentary system or impeachment under the US Constitution. In theory, a very hostile President/Congress relationship could have the President removed through impeachment. It is only our norms and traditions that have kept that power from being truly realized, but it is an absolute power. The courts cannot touch it and the President cannot issue pardons when impeachment is involved. If the impeachment of Andrew Johnson had resulted in conviction and removal, it's quite possible it could've transformed into a de facto vote of no confidence.