I’ve had electric (first wire, now poly rope) fencing on trees for decades - and Wellscroft Fence in SW NH has high-tensile on trees (for sheep, not horses), so it’s not just me - and I don’t find either of these points to be true.
Nor do the trees that I find with old fence wire (field fencing or barbed wire) embedded deep in them (some dating back the better part of a century) look at all damaged (though a chain saw blade might be if they’re cut carelessly!). And last year when rebuilding my fenceline from the '70s-'90s I found a number of old plastic insulators which I’d nailed directly into the tree, some 1/2 buried, some completely surrounded by a healthy tree with just a plastic disk (the top of the insulator) visible. The tree seems to grow around it just as it would a dead branch stub.
Now I know that the fencing will be maintained more easily if the insulators (assuming electric here) are attached to a board - some use 2x4, I use 1x2 or 1x3 - and that board nailed onto the tree with fender washers under the nailhead. The board should then be pushed out as the tree grows.
I also find that doing this makes it easier/quicker to attach the insulators to the board and get the spacing right, as I can do that in the barn where I just mark all the boards in advance and run through them putting an insulator at each mark.
While I don’t notice the trees moving much as close to their base as the fence sits, electric fencing should move freely through its insulators so what movement there is shouldn’t cause strain on the wire. I suppose theoretically this could cause abrasion on today’s poly rope, but in real life, I haven’t seen any problems, at least in the 7 years since I first put a poly rope fence on trees when my sister got horses again. The 14-gauge wire fence was maintained for a couple of decades, 1977-1996.
I have problems from fallen trees/limbs, large animals (moose, bear, maybe deer) going through the fence, and water-swept debris, but not from the trees that the fence itself is attached to (unless they fall over, which is rare, but sometimes a dead tree is in the convenient spot and I use it for as long as it will last).
I will always use a tree preferentially over putting in a post. Especially in our intervale (=floodplain) field, every corner and gate has to be braced even for low-tension wire because the ground gets so soft when saturated, but trees brace themselves (roots!) and save me a lot of work.
Plus - and this is a new one to me; I just found it out last winter, my first with a poly rope fence (vs. wire) out in the field where there are no trees - with snow/rain/freeze/thaw/freeze cycles, and poly rope instead of the thinner wire, the snow’s crust will freeze around the lower strand(s) and then as it settles it will pull the T-posts and fiberglass rods (I use a combination) deeper into the ground in the soft silt. Last spring I had to go along the fenceline and pull many of the fenceposts up by several inches. In the woods, with the same soil, where the fence is on trees, I just had to clear a few branches.
Wow, I can’t believe I wrote that much about this! But I’m proud of my fences, which I keep snug and neat, and I’ve had nothing but good experiences using trees as the posts, at least for the low-tension electric fencing I use.
