Almost all plants have value in our lives.
Most plants and trees are edible, provide shade, and help add oxygen to the air.
Trees provide a place for mushrooms to grow.
USDA said, Through a process called photosynthesis, leaves pull in carbon dioxide and water and use the energy of the sun to convert this into chemical compounds such as sugars that feed the tree. But as a by-product of that chemical reaction oxygen is produced and released by the tree
I have never owned a mulberry tree though as a child these trees left the sidewalk with dropped berries which I remember being messy to walk on.
To answer the question:
"What's that one plant that annoys you?"
I would say mulberry trees, though it has been many years since I have seen one.