Boy, can I relate to Grumpy Old Man! I could have written that letter a few years ago before our fence went in.
We had the exact same problem. I posted the entire fence saga here. We moved into a house that was not fully fenced. It was known in the neighbourhood as a cut through point and just like GOM, kids were in and out, back and forth numerous times per day. At first we didn't mind because it started out as the kids behind and the kids next door going to each other's house. More and more, we noticed other kids going through, and parents as well. We would find random people and kids in our driveway, they would dart out from our front yard into the driveway when I was backing out of the garage. We even had kids ride their bikes on our lawn. With all this, we started to resent the intrusion and lack of respect for our privacy and property.
When the fence started going up, the mother behind was storming through her yard, making it visually apparent she did not approve of the fence. Another neighbour approached me and said she got phone calls expressing concern about our fence and 'did they overstay their welcome?', to which I replied, 'yes, it got to be too much and we want our yard to be our yard... besides, we have a dog!'. Never mind that someone complained to the city about the height of it being 2 inches too high in spots b/c o the slope in the ground - dh built it to be even on top instead of the bottom. He had to redo it.
She then laid the guilt trip that the previous owner gave her kids a 'safe haven' to cut through instead of going around the corner. It was absolutely ridiculous.
We never said anything to the neighbour kids who did that. But the stranger who had the audacity to ride his bike through our yard and the kids we never saw before we told to get out and stay out. The problem with the neighbours is they never asked. They assumed. They took advantage of our newness to the area. Because we never said anything, the growing intrusion made us resent them and everyone else. We wanted our property back.
The straw that broke the camel's back was when mother behind came through the yard, walked across our driveway, DH was working in the garage and she said a smug hiiiiiii... dh felt like a lawn boy on his own property. The fence started going up the next weekend.
We put "NO TRESPASSING" signs and pilons in the back and front when the post holes were dug. We wanted to prevent any type of liability issues of someone cutting through getting hurt. Mother behind took that as a notice to them and got on the blower to the other neighbours about it being directed at them. I guess in a way, it could have been, but the ultimate purpose was to ensure no one got hurt.
GOM has the right to institute any limitations he desires for his property, especially when they have taken so many liberties. I would be ticked if every other ball went into my yard too.
All he needs to do is talk to the kids and explain he is getting tired of the constant back and forth and to please stop hitting the balls into his yard. If that doesn't work, then he needs to talk to the parents.
I don't suggest he hold onto the balls. That made it to the news and has been discussed here a few times. That is a PA way to handle the situation, BUT if he talks to the kids and the parents and the problem still isn't resolved, then I see no problem with him keeping the balls, but only after he has tried all other solutions.
ETA: There was a thread recently on this very subject - balls in neighbour's yards. Got very heated. I am a horrible searcher, so probably can't find it. I'd say it was about 6 months ago and maybe someone else who remembers the thread and has good search skills can find it. It was less than a year ago I would say.