|What makes poison ivy so insidious is how well|
it blends in with its surroundings
The thing that makes poison ivy so insidious, is that it's a master of camouflage. Amid Virginia Creeper, it will have dark leaves with serrated edges that look like Virginia Creeper; if it's growing amid Cross-Vine, it will have lighted-colored leaves and less noticeably serrated edges. This is a good example of selective evolution at work. When we kill the poison ivy we can spot, we leave behind the poison ivy we can't spot, over time inadvertently breeding species that blend in more and more successfully with their surroundings. Eventually we will make it impossible to ferret out at all; it will be indistinguishable from common ivy, blackberries, even oak trees. Everyone has had the experience of breaking out in poison ivy welts, having been unaware of having been in poison ivy.
I think the solution is to deliberately cultivate poison ivy that is easy to recognize. Instead of killing the poison ivy we can see, we should only spray the plants that are the most difficult to detect. If we see some poison ivy and think, "Whoa, poison ivy," we should leave it alone unless some other poison ivy comes along that is even more conspicuous. I'm not saying this would happen overnight, and indeed generations would melt away before the project was complete, and - most importantly - we would need 100% cooperation from every person on the planet, but if we stuck to it, gradually poison ivy would become absolutely impossible to overlook: it might have bright mauve leaves with pink speckles, ideally with the words, "p-o-i-s-o-n-i-v-y" right on them.
Then, and only then, on a pre-agreed signal, everyone would go out on the same day and spray the poison ivy into extinction.
End of story.