It’s hard to get a visual picture from a text description, but it sounds to me like you’re upset becuase the neighbor isn’t mowing your grass? Please tell me I am wrong. No matter how “easy” it would be for him, it’s simply not his job. Please tell me I am interpreting this incorrectly!
Nah, I agree with the OP. We just got new neighbors over the winter, and when he started mowing, he MOWED a strip on my side of his driveway. We’ve always mowed all the way TO his driveway. Well, I’ve got a kid doing my yard now and he saw the difference in grass heights and kept up the weird boundry the neighbor established. (I have no idea where the actual line is. I actually assumed it was driveway to driveway.)
However, the neighbor on the other side mows all the way to my driveway, though clearly if you look all the way to our back lots, you can see that my yard actually goes those few feet over on the other side.
I’ve really been wondering what to do about the mowing neighbor. That strip looks stupid, like the OP says, because we mow on different days. I’d be willing to talk to him about it, except I’m scared of him now, after he yelled SHUT UP out his back door one night when my dog was barking at 11:30 pm. (He has 3 dogs, BTW.)
Whew, that was a rant I needed, too! 
We have a so-called “strip” on the side of our driveway. My dad got in a fight with the previous neighbours when they moved in and started mowing driveway to driveway and part of our yard.
The main reason he was pissed was that the neighbour tended to “scalp” the yard so he would have to mow less often, and while ours was nice and green, but had to be mowed more, theirs was brown, short and spikey for the most part.
So I am definitely in the camp of talking to the guy about it first.
Look, I think it’s fine to mow driveway to driveway as long as it’s OK with both parties involved. The practice makes a lot of sense.
What bugs me is the assumption that the neighbor ought to as a matter of course (and thus is an asshole for not doing so). I would not, personally, for the reasons I and others have given - unless we’d talked about it.
jinwicked’s experience is a great illustration of one person’s “help” being another person’s “pain in the ass.”
I have a problem neighbour myself (see my thread in the pit about her cat killing my tree if you like), and I sympathize with the OP. It seems like he’s getting worked up about a small deal here, but with neighbours like mine (and probably his), a lot of small deals add up to some big annoyance. For example, our neighbour has junk all over her yard. Her yard, she can have as much fast food garbage as she wants on it, right? Except for the part where I end up picking it up because it blows onto my yard.
Some people are just asshats, and that’s the way the world is. And I agree with the OP that this is a good example of what’s wrong with the world today. It’s a great example of the “I got mine - screw you” mentality that we all run into every day.
I’ll mow your 4 feet for $60. Plus expenses, of course.