Yeah, it also assume that the pile you're driving can be arbitrarily long and will last forever. They used to be made with trees, for which this is obviously false.
It depends. Fully soaked ground will actually preserve wooden piles (wood decay is aerobic and requires oxygen). This is why Venice and New Orleans are both built on them (sinking issues aside because they have other issues). The piles in both cases are quite stable because the ground is completely soaked. Where you run into issues is where water and air meet. I would imagine wooden piles in just water would have issues with shipworm (in appropriate venues). But the ones in fully soaked soil seem to last just fine.
I suspect, but don't have data on, that wooden piles may actually last longer in those exact circumstances due to galvanic issues with concrete and rebar or metal pilings.
It looks like a layer of plastics, so I would expect not well. Though, the part you'd hit would be above the ground, so it might still protect pretty decently for all the below ground stuff. You might consider putting a small set of stones around it so that the trimmer cord hits those instead of the wrapped wood.
Should probably just do a layer of stones under the whole fence... then you'd get that benefit for all of the boards that are close to the ground and not just the posts.
Not to mention that wooden piles were often treated with an absolutely massive amount of creosote, to the point that a number of timber pile treatment yards are superfund sites.
But they don't last forever, so a lot of them are being replaced at the moment. Expensive operation as they have to be replaced in-place, but Amsterdam canal front houses are prime real estate.
