This is a beautiful explanation! It is short, and clear.

However, one of your lines on map 4 is incorrect. Both this map and the Mercator projection would have a straight line from New York City to the North Pole, like all the other meridians on both maps. (Meridians are halves of great circles, and are also drawn as straight lines on both maps.) This is one of two exception classes: a North/South rhumb line is along a great circle, as is any rhumb line along the equator. No other rhumb line is along a great circle path. Thus:

All rhumb lines not following the equator, or not following a meridian (N/S line) are not great circles, and are not the shortest path.

This also modifies the conclusion.
“However, a rhumb line is not the shortest distance…” is more accurately stated as:
“However, a rhumb line is RARELY the shortest distance…” Other fixes also work.

(If you make this change, straighten the line from NYC to the North Pole, explain the two exceptions, and change the concluding text to “rarely’, “not usually”, or another more accurate description, I will be grateful. I like referencing your clear work. Thank you!)