Cutting it will unbalance the tree
Really? Perhaps a young tree, but an established tree with roots? Maybe maybe not.
We have a lot of ivy covered tree’s in our area, mainly big oak’s. The ivy always looks like it’s strangling the tree to me, inhibits leaf growth and ensures the early demise of its host. So I say cut about a foot or so from each vine a little way up the trunk of the tree. I would say that the tree is happier for it.
Take the point about pollen and bee’s.
The gamekeeper likes it because it can provide roosting cover for his pheasant’s and partridge’s. Although they all seem way too happy being on the ground and doing as little flying as possible. Probably because they know what happens when they do fly 😉