Not a week goes by when I don’t deal with Ivy in trees.
It is one of the most commonly misunderstood interactions between one plant and another despite the fact that the interaction of Ivy with trees is well-researched. It can take years for views to change as the knowledge enters every-day wisdom.
The facts are that Ivy does not strangle, compete for water or kill trees.
Ivy may become dense in the crown of a tree that’s already dying back through old age, damage or disease. It may need to be controlled. But there is certainly no imperative to remove it.
I take a pragmatic view. If it is increasing the ‘sail area’ of a tree’s crown, or I want to more-closely inspect the structure of a tree; then remove it.
Otherwise, leave it for habitat and a late nectar source for bees.