We have a lot of the wooden poles in our fields, and also one of the big giant steel strutures, although thats well away from the house.
One of the posts was right next to the house, blocking the way round the back. The electric people came to renew the posts a while ago, and they did put some wires under ground. Because they were there, and renewing the post anyway, I asked how much it would be to move it a few feet. I know its usually costly. Anyway, the kind men said as it was being renewed anyway, they would move it the few feet out of the way. OK, I can see it from the house now, but at least its out of my way.
I think they will move a pylon, but at a cost, and probably only if they think its for a good enough reason