An industry built on cutting it back
The reason willow has been grown deliberately for thousands of years is not its timber. It is that cutting a willow hard makes it respond with a dense crop of long, straight, flexible one year rods, and it will do that indefinitely without being harmed. Cut it to the ground each winter and it will still be producing a century later.
Those rods are withies, and basketry ran on them across Europe and Asia for as long as there have been baskets, along with hurdles, fish traps, eel pots, coracles and fencing. Whole landscapes were managed for it, and some still are.
The color comes from the variety and from the processing rather than from dye. Cut and dried with the bark on gives brown. Stripped after being stood in water until the sap rises gives white. Boiled in its bark before stripping gives buff, where the tannin in the bark stains the wood underneath. A basket in three colors is one species handled three ways.