The only check currently seems to be people disobeying his orders, and even that is accounted for to some extent (see "mutiny is unlikely" in the article you cited).
It remains possible that ranking members of the executive branch and military might cooperate to make sure the president is isolated and unable to execute the protocol, and perhaps even conceivable (if unlikely) that enough of the military would refuse to participate. But that's the only real check, and it extralegal rather than any part of the system.
If you've ever been suspicious of "the deep state", think about that for a minute here, because it's really just another catchy term for the one of a half-handful of checks on the power under discussion here.
> I think the trope stays around because people, despite what they say publicly, like the idea of an emperor style president with supreme power.
I suspect that people really want to believe the system works, it can't be that messed up, someone else thought of this, some one else is paying attention, and they want things to be better, not worse, and they will take care of it for you.