I wonder if those metal joist hangers were too high-tech for the Amish

This is indeed the strangest Romex installation I seen.
It can also be a hazard if a dog chewed on it. I had a dog that chewed on the wood trim around the doors, I am sure she would have chewed on the Romex if it was open like that. Also a small child may pull on it. The guard strips are a good idea, but will need to be covered to protect it from sunlight.

It would be good if the code was more specific, like any Romex exposed less than 6 feet from the floor needs to be protected. That will solve the judgment question of "subject to damage" in many cases.
I imaging some local codes may say that. It doesn't really apply in my area, since Romex isn't even allowed at all.

I would take a step back and say - needs metal raceway system.

If it was that simple.
Now I know the rest of the story.

The list he needs is long.

1. Building permit.
2. Stamped plans.
3. Framing inspection.
4. Insulation inspection.
5. Footer inspection.

So I guess the electric is a small problem in the end.

For the framing and insulation inspections they will need to remove parts of the finished walls, maybe they will think about running the wiring in the walls, depending on how many sections of wall boards need to be removed.

Then you may wind up in jail, LOL

What the heck is that rafter(?) doing there with nothing else in sight?

And what is an Amish cabin? I lived near an Amish community in Sarasota, some pretty damn good carpenters there. I think they'd be mighty upset calling that an "Amish cabin", LOL

They built portable cabins. They drop them on site you finish.

Or they drop it ready to power and PLUMB and it is a "hunting cabin".

http://www.woodtex.com/cabins.asp

We do all their in plant inspections.

Those bottom three are called "log homes", LOL.