If the president is incapable, as Nixon was in your description (and in https://www.alternet.org/drugs/huge-role-alcohol-has-played-... linked down-thread), then there's a procedure wherein the VP takes over, isn't there? Not performing this procedure is deciding to contradict the democratic will of the people.
Now, I can see how you might not want to publicly remove the president in a military crisis situation; but the way it was done seems completely wrong, just assuming power without due process, countermanding the president whilst they remain the president .. (as Nixon was CinC surely that's reason for a Court Marshall?)
Did the people ever react to that, have anyone punished? Or are the USAmerican people happy to have a VP secretly assuming power, a Secretary of Defence that chooses when to obey orders, etc?