Sure why not have a little space on handouts dedicated to campground etiquette? Something written in a cheerful helpful way-maybe with some stupid cute cartoons etc. Or have a silly/cute bear cutout on the side of the entry road displaying a new etiquette tip daily? "Coco the Bear says...." Even if it is just a small percentage of campgrounds who do, it may help. I think some of these problems such as cutting through sites are done out of ignorance by some people. One other idea is to incorporate campground design to help with problem. Natural vegetation or some demarcation to separate sites. Best example I have seen is at El Moro campground with small low wire fences separating sites. And I saw no one cutting the fences in days of staying there.
Of course not all will be courteous campers. But I do think there is a subset currently who would do better if they knew the etiquette.
Back in the "good old days" in 1950s we had a bad littering problem here in southern CA. I remember as kid a lot of lessons, films etc. on this subject. Emphasized leaving it cleaner than you found it. It always stuck with me. Aim some of this at the kids.