I'd like to know whether others would even bother photographing a lone fence post like this one; and if you would, how your approach would differ?
Well the first question is hard to answer. All I can say is that I would know it if I saw it.
In that case, if I thought a lone fencepost such as this one was worth photographing, my approach might differ in two ways:
1) Show the whole post, but give it more space to breathe. It should feel alone, but not crowded. Also, provide a background that does not distract. The background area in your photo #1 is too small and it consists of two contrasting values, the darker of which is too similar in value to the fencepost. So, for example, I would like this better if there was more room around the post and the background was a large field of light-colored grass (like is present in the bottom area) with a plain light-colored sky above.
or...
2) Move in for a close crop as in the third photo, but light the subject better and again, provide a background that is a different value from the subject. In this case that background should also be out of focus with no distracting bokeh.
(I don't think I ever figured out what such a photograph could be about.)
As time goes on, I find more peace and satisfaction in not analyzing, but just listening and going with my intuition.