Being at war with a plant often means that this very plant wants to tell you something. I used to be on a war against broom and a few other plants, and then learned about their medicinal properties and practical use. After getting to know my enemy well and respecting its function in the world, I managed to let go of that 'Eliminate!!' view of things and become way less frustrated.
Which made it possible to think about more long-term solutions:
On a landscape perspective, could you offer your landscape an alternative plant? Just removing something will usually not work because landscape wants cover, but sometimes you can plant something else in the same space that will gradually crowd the privet out or better, force it back into a more manageable space. Find some use for the privet - a quick Wikipedia search finds that 'The decoction of privet leaves or bark helps to treat diarrhea, stomach ulcers, chronic bowel problems, chapped lips, sore mouths and throats, and a wash for skin problems.' (Please do some research before using a plant medicinally and start with tiny amounts. Careful the berries are mildly toxic)
For gradual removal, you can alter the composition of your soil (a gradual work) so the privet doesn't like it anymore. You can get help from allies like other plants, animals, fungi, microorganisms and add certain organic matter and/or minerals. A gradual process that will bring you very close to your landscape.
I believe quick and genocidal solutions against plants and animals who often have lived on 'our land' for longer than us is very old school. Getting to know them first and asking them politely to cede more space for our activities should probably be the way to go in the future.
Dude, we're talking about a highly invasive Asian plant growing in North America. Birds rapidly spread its seeds, which germinate in natural areas and choke out/kill all sorts of native North American plant species. If this were a native species, the advice given here would be much different. Invasive Ligustrum lucidum should always be removed in the US
Privet also does just fine as a hedge, and people in the UK actually use it for this purpose. Ironically, that's where I've seen privet growing—along borders, so people who hate privet might as well leave the stuff unless it's in their way.
I live in the Southeastern US. It was originally introduced here as a hedge plant as well. Unfortunately it's gotten wildly out of control and is very invasive. It crowds out other plants, cultivated and wild. I have a Jerusalem artichoke plant that it has a stump in the middle of and it keeps trying to grow higher than it to share it out.
I very much would like to never see any privet again in this area. Along with mimosa, tree of heaven, and kudzu. If you can't tell already I'm from the Southeastern US, haha.
It is an uphill "battle" and yeah, doubtful I could win in actually removing all these plants for good. It's frustrating to see how they destroy native plants that are useful and important to me and the creatures around me. I do think they have an overall negative impact on the biodiversity of the area, but I didn't know about its medicinal uses. It's easy to get into that mindset that it's entirely negative. But you're right, I've gotta try and see it holistically.
My main gripe with Privet in particular is that it's growing in the middle of other plants. I've got a Jerusalem artichoke, fig bush, and scuppernong bush it's trying to crowd out. I'd be worried about altering the soil composition for the sake of the plants that are already there that I'm trying to save.
It seems that its favorite place to grow is in disturbed forest, but it's a very opportunistic plant and will grow outside of that, including in other plants. Sigh
Edit: I didn't mention explicitly that it's an invasive introduced to the area along with the other plants I mentioned. Just wanted to clarify that.
'Uphill battle' describes it quite well. I fought my invasive mimosa, at first just by cutting, then by cutting and burning, then with roundup. I never even had a chance. There are so called invasive species filling our rivers, growing in our forests, covering whole buildings. The battle is long lost, they will never return to their homelands and stay there. Also true is, at least with invasives in Europe, they don't really invade untouched and natural landscape - but landscape which we have emptied, mined, grazed, chopped clean, burned, planted (often with these very invasives), polluted ...
There is something in this 'invasion', 'war' and 'battle' metaphors leading back to people, and the way we try to keep undesired people out, and my perspective towards invasive plants has changed since comparing the two.
I think we have to come to terms with that in the moment our ancestors started wandering the earth they started to carry other animals, seeds, plants, microbes with them. Conservationism and removal of invasive species follow a logic that this process should have stopped at some point. I can completely understand the sentiment behind that. I wish colonialism had never happened. I wish no invasion had ever happened. But they did, and we all are the result of it. I can't even imagine what would happen if we had a magical box, could turn the dial back to a date, and every species, every tribe would return to what were their homelands in that instant in time. But to what time period would we want to turn this dial even? What is the one true glorious point in the past we should all return to? By this logic, there would be no place to return to for many 'mixed' people, animals and plants.
So there is something unresolved, unsatisfying about the term 'invasive species'. The idea behind denies the dynamic, changing, ever moving quality of all life.
I'm sorry if that helps very little with your privet. Another suggestion for the privet would be to research how it grows in its place of origin - what soil, what plant community? Maybe there's something there you could work with.