Trees are living things and will shed old leaves, twigs, nuts, seeds and flowers as a part of their normal lifecycle.
The trick for managing that is to understand the habits of your tree and plan maintenance accordingly. For example, if your tree is deciduous, you should plan to clean the gutters during and at the end of autumn as this is when leaf build up will occur.
Products such as gutter guards and pool covers will also help to reduce the impact of falling leaves and twigs.
Material falling from trees is not considered a reason to remove the tree. Just as lawns need to be mown and garden beds weeded, sweeping up under a tree is a normal part of home ownership.
Case study
Anne has a large Gum tree in her garden that drops leaves and twigs onto the lawn. They get stuck in the lawn mower and the shade from the tree stops the grass from growing properly.
Anne decides to reduce the amount of lawn she is mowing and creates a garden bed under the tree. She chooses the plants for the garden bed carefully and finds there are lots of things that will flower in the shade of the tree. The falling leaves and twigs don’t bother her now as she considers them to be free mulch for her garden.