I have a rather nasty rash. Fortunately it is one of the few socially acceptable ones: poison ivy1.
I got this rash visiting my dad’s place in the country the other weekend. He lives just across from the middle of no where, and with all the woods surrounding poison ivy tends to make its way towards the inhabited parts of the property. Worse (from my perspective) dad is hardly ever affected by it, so it tends to get ignored till I show up.
As it turns out, there is an interesting solution to the problem of poison ivy: goats.
They apparently love to eat that shit. Of course they do. The laws of gravity are apparently largely optional for them, so why wouldn’t they just decline to care about rolling poison ivy around in their mouths?

Now, goats are not perfect for removing poison ivy. They will merrily eat all the leaves and stems2, but they don’t dig up the roots so you have to either do that yourself or let the goats keep eating over time until the roots run out of leaf power.
There is another, bigger problem with goats: they don’t just eat poison ivy.
That’s fine for the patch growing up the front of the workshop, or the patch growing by the lumber stack in the paddock. It’s rather less fine in the garden area where poison ivy is clustering below the lilac bushes and intermixed with the vegetables.
Goats are gonna goat, and while they might prefer to eat poison ivy over all those other options, we know from experience they are going to get their little goaty lips around other plants we want them to avoid. Even the most well intentioned goat can’t pass up a nibble at the occasional tomato or cucumber.
So, what to do?
I mean, sure, we could go out with long gloves and a shovel and hand remove the poison ivy ourselves. Plus side, that gets the root and everything, and if I get peckish and nibble on a tomato, well, that’s what those are there for. Down side, you have to spend a lot of time stooped over digging under bushes and all, plus the plant you are digging up wants to put its evil inside you and will do so at the merest brush of exposed flesh.
Assuming we don’t want to deal with a rash3 when we can assign goats to the task, we do have some options.
At one extreme, we can just say “hell with it, poison ivy is bad enough that I don’t care if goats just eat everything if that is what it takes.” We can just give up on having a veggie garden (and lilacs, probably) and let the goats do what they want to make sure there is no poison ivy left. If the area was small enough that the kids couldn’t go out to play without getting a rash, or if they were super sensitive, and thus we couldn’t use the yard for fear of poison, this might be a good idea. (Assuming goat poop didn’t make the yard unusable, either.)
Another option is to put up some serious fences to limit the goats’ reach. This is tricky, primarily because keeping goats contained when they don’t want to be requires dealing with that “gravity optional” aspect. That might require a lot of work putting in fencing, or tethering individual goats to posts4.
The other tricky part is dealing with the areas you keep the goats out of. Limiting the goats’ access means increasing the amount of demon ivy you have to deal with, either via removing it yourself or just accepting its presence. In the end, there is always a tension there. If you aren’t willing to let the goat just eat everything down to the ground, you have to spend some amount of effort fencing and then digging up or avoiding remaining ivy.
To put it another way, either you
Dig up everything yourself with all the associated costs5;
Put the goats in charge and let them consume everything down to the turf;
Spend a lot of time, money and energy limiting the goats' scope of control, constantly enforcing and correcting that scope, and are still be left with poison ivy to deal with yourself.
Now, with that last one you can make many different trade offs between how much the goats are allowed to get to and how much effort you want to put into controlling them vs solving the problem with your own hands. That’s just it though, it is a trade off, and part of the trade off is constant vigilance and correction. You don’t just get to put in a fence, put in the goats and job’s a good ‘un.
Why? Well firstly, goats are clever little devils who, as previously mentioned, have only a passing association with gravity. They also have lots of sharp hard bits that they use to work around those few things they can’t climb over or under. Also, this sort of thing:
If it seems like a good idea at the time to a goat, the goat will find a way given enough time.
Additionally, goats tend to multiply. Eventually you will find you have more goats than you want, and have to figure out a way to cull the herd a bit. The trouble is the goats themselves don’t like this much. More troubling is that often non-goats don’t like it much, either. My girls are pretty clear on what chicken is and where it comes from, but I don’t think I could get away with roasting Bob the Goat once the girls have got to know him, and certainly not “Beardy the Kid” when he is still young and cute. We all might agree that there are way more goats than is desirable, but picking out specific goats to oust is difficult.
Another, non goat, problem is that while the goats obviously want to find new and exciting ways to goat, poison ivy does too. Granted, “new and exciting” to a plant is rather less so to a human, but that doesn’t stop the plants. They will move to new areas, flourishing in all those spots even a goat who can phase shift through a fence can’t reach. We soft, fleshy and eminently rash prone humans need to keep up, either increasing our manual tasks or constantly readjusting our goat containment methods. Even if the goats are given free reign, new vines will sprout up now and again and cause the very problem the goats are meant to correct6. We simply cannot live in a world without danger of poison ivy.

There will be costs either way, that’s just economics. Moreover, it's just reality. We either deal with the problem ourselves or deal with the problems of letting others deal with the problem, which will include some dealing with the problem ourselves, anyway. God created poison ivy, goats and humans7, so here we are.
There is one option, however, that we know won’t work: talking the goats into just not eating everything else. I mean, obviously, right? Goats are going to goat, and so we know that goats are going to eat everything they can reach according to whatever inscrutable hierarchy of preference they follow. It isn’t a question of getting the “right goats”; some goats might be particularly bad about it, maybe hating the taste of poison ivy or loving spaghetti squash, but any goat is going to eat what it can get to. Even if there were a goat who could honestly claim “I am on a strict poison ivy diet. Veterinarian’s orders!” it would behoove every other goat to make that claim as well. Being clever, you know the little slot pupiled buggers would do it, too.
The question then isn’t getting the right goats, or attempting to change the nature of goats. Goats are goats, and what is left to us is identifying the situations where they are useful and beneficial, and working very hard to keep them out of the situations where they are not. Putting the goats in charge is fine if you really don’t care about having only those things that goats do not care to eat, but if you think “This time will be different!” and expect them to keep their little goaty lips off your beans, well, you deserve to have your beans eaten by goats and lesson learned.
The question is always “Is it better to deal with all this myself, or deal with having someone else deal with some of it for me?” You can’t solve the problems, but you can trade some problems for other problems. The decision is about what problems you would like to have.
For myself, I plan to dig up some poison ivy. I think goats tend to create more problems than they solve in this situation, and once you have them and learn their names, it is really hard to get rid of them without someone crying. Let alone eating one.
However, I do appreciate that goats don’t ever get in league with poison ivy. Regulatory capture is apparently just beyond the capabilities of goats and poison ivy.
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It is ugly and uncomfortable, but fortunately doesn’t come with moral sanction.
Maybe not the woody parts if it grows to vine form, but then goats, so maybe?
Being highly rashional.
Which itself can be a miserable piece of work depending on the size of the goat and how inclined they are to get tangled up.
I am ignoring herbicides here, as they have many of the problems of goats: killing plants you care about indiscriminately. Plus they also don’t match the meaty four I am targeting.
Because they can only correct, not prevent. They can’t eat a plant they don’t know is there, and finding it takes time.
Possibly not in that order. One does hope that He didn’t make the invasive plant species, that seems to only target humans with an itchy rash as punishment for brushing against it unknowingly, after humans, you know, on purpose, knowing what it does…
In regards to tethering goats to post, a viable option you may not be aware of...
A tip I've noted, as an aspiring goatherd myself, is to place on the rope a PVC pipe (or maybe a length of mostly straight PEX would work too) about 12"-18" down from the goats collar and about 12" from the post or lead spike. Tie stopper knots at each end of the pipe to keep it in place on the rope. The rigidity of the pipe prevents the goat from getting tangled in the rope along the length of it where that is most likely.
see: https://www.youtube.com/watch?v=5AwutafIbbk
You forgot a solution: find a human with natural immunity to poison ivy, pay them to remove it.
Although personally I'd be fine with letting the goat consume everything in the garden down to the roots, and then eating the goat instead of the vegetables.