Now that's what I call Ivy. Common Ivy (Hedera helix) eventually forms a main stem more like a tree trunk. As I've noted before Ivy is an ecological treasure trove. Ivy in flower attracts around 140 species of insects. Even in early November it still hums with wasps. Likewise the berries are food for birds and Ivy is a food plant for the larvae of certain moths and butterflies, not to mention a habitat for insects, birds and small mammals.
Having said that I do cut Ivy back because it can be invasive at the expense of other plants. I wait till it has flowered and leave a decent amount of thick growth for wildlife value. In the example shown above I ran a hedge trimmer along all the trailing vines which had completely obscured the wall but left the top knot.