Set the legality of trapping aside for a second and consider the reality of trapping and dogs... You cannot convince a dog owner that potential dealth by trap is a reasonable penalty for their dog being off leash. Fines, sure, but not death, because dogs are family members.
Therefore, with so many dog owners out there, trappers need to consider the PR repercussions of placing kill traps near trailheads, even if legal. A few dogs trapped and killed with raise enough negative PR to get even non-dog owners to rally against trapping.
The general public will largely favor a cute dog over a trapper. Trapping near trailheads may be a right, but it puts you in the wrong as soon as a dog is injured or killed, and this is the fastest route to outright banning of trapping. With increased outdoor recreation and the growing influence of social media, it seems that trappers should put in extra effort to not create negative PR, and this might just require giving an inch to retain a mile, so to speak.