I miss home teaching and as a home teaching coordinator, was one of the best experiences of my life. But the emphasis and importance, I have noticed, is different from stake to stake and ward to ward. It shouldn't be that way, but it is. 7th Ward, in Glendale, California placed a special importance on home teaching. Maybe that's why I feel the way I do about it.
During the time I was inactive, I would request that the home teachers assigned to me would still come and visit. The problem was a person can tell when an individual is just going through the motions because he/she has to fulfill the obligations of their calling. My wife and I asked ourselves what the point was afterwards sometimes because we could tell that the priesthood holders administering the lesson's heart and spirit was not really into the visit. And that if choice was given; they would rather be else where. And in truth, was one of the reasons I had problems transitioning from a ward I was so attached to in California, to the unfamiliar Chicago 1st Ward. I can tell you that having home teachers that showed genuine interest in my spiritual and overall well being during that transition time would have helped tremendously.
Sorry for the long post. Point is in home teaching, is don't fulfill your calling just to do it and get it out of the way. Take an earnest and genuine interest in the families you are responsible for. Instead of that phone call, show up at their house and show that that you care. And for that difficult companion, I would speak with EQ President at some point, but I would like Rico said find ways to fulfill you calling. Just make sure it's for the right reasons.