Whether you're a proponent of Scalia's textualism or Breyer's pragmatic constitutionalism, the obvious answer is that, yes, the Cabinet is able to invoke Section 4 for whatever purpose it deems fit
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.
Well that’s why the 25th still requires Congress to take action, with a two-thirds majority in
both houses, in order to make the removal long-lasting. So an ambitious VP can’t just use it to stage a coup if he disagrees with the President. But in an emergency where there’s no time for a formal impeachment trial, the 25th absolutely makes sense as a temporary stopgap measure.