I think that if you want a postcard photograph, a nice technical exercise that looks exactly like 19282938 other pictures of a tree in some fog, by all means clone the wire out.
For me, I'm not sure that the photograph actually works this way but I see that it COULD work this way: The wire draws the eye, reminds us of man's presence, and then the rest of the scene fills in -- the fenceline, the plowed earth in the foreground. All these details are a bit subtle, and can pass unnoticed, leaving one with a vague impression of a pretty tree in some pretty fog, yawn, can I order 1000 of them to put into the rooms of my budget hotel chain please?
With the wire it might fail, but it aspires to be something more than a pretty picture, of which I feel we have far too many already.
Edited to add the attachment. This is, I like to think, similar in feeling. Also, it is a complete nothing as a photograph. Sure, it's tolerably well balanced, there's the bird which makes things more interesting, but there's nothing there. The picture functions as a snapshot, it exists to remind me of what mornings were like when I visited my friend at his rural home last summer. I flatter myself that it's quite a nice snapshot, but that's all it is.