For the Cabinet and the VP to initiate action would be a momentous move, and some would consider it a coup d’etat, but it IS one method available.
I see this as something that would happen only in the event of the President becoming physically incapacitated, and he was either willingly going or else he was in a coma in which he couldn't say or do anything.
But, I don't ever see this being done against a President's will when he is fully physically capable and mentally capable.
There are also things in the Constitution that I don't ever see as happening. I was just on another thread where they were talking about the states invoking a Constitutional Convention to make some changes to our present form of governing (as we conservatives see it happening right now).
The only trouble there is "opening the door" to a Constitutional Convention (which can be done) will open the door to all sorts of liberals and Marxists making changes to that same Constitution, too.
So, I never see this one as happening in our futures, either.
The Amendment you've brought up isn't going to happen (be put into action) with a President that is physically and mentally capable of discharging his duties and he's "taken out" by this Amendment... no way... :-)
Never say never.