I spent quite a bit of time embedded in the Permaculture movement and have heard all these arguments before. I have read all the key Permaculture texts (both volumes of Edible Forest Gardens, Mollison's original Permaculture: A Designer's Manual, and many more).
They do not mesh with ecological science.
The problem with Permacultrure is that if you pay attention to the design system, it's effectively a return to pre-science individualistic naturalism. It's entirely based on individual personal observation, and removes a lot of the checks against personal bias that science introduced to improve upon individual naturalism.
Thus it's entirely possible for a Permaculturist to observe invasive species doing useful things for their ecosystem and completely miss all the damage they're doing. It's easy to see the the squirrels who use the Honeysuckle for cover and the birds eating its berries and completely miss all the Lepidoptera species that would be eating the plants the Honeysuckle displaces, and all the birds that depends on those species for protein. This is what Permaculturists consistently miss, but the ecological science is very clear about. Invasive species do far more harm to their biospheres than good.
So when Permaculturists discount controlling those species they are failing to do the very thing they claim to be attempting to do: build healthy ecosystems.
All too often with Permaculture it's much worse than just writing off the need to control invasives. I have seen Permaculturists become so obsessed with designing novel ecosystems that they even introduce invasive species.
The goals of the Permaculture movement - building a society that exists in harmony with the natural world and is thus not only sustainable, but regenerative - are sound. Many of the ideas - building agricultural systems that act like ecosystems - are good and worth exploring. But the methods and approaches taught by Permaculturists in PDC courses are deeply problematic.