Privet is one of those invasives that needs to be managed, but might not ought to be totally eliminated. It can and will take over, but a little of it is okay. The excellent and highly recommended "Trees of Arkansas" book published by the Forestry Service is typically very dry, like most government publications, but it injects a bit of caustic value judgement about privet. "No economic uses. A pest to the forester...."
Well, okay, but birds eat the berries, rabbits nibble its shoots and hang out in the thickets, and archers can use it for arrows and, if you can find a decent sapling, quite fine bows.
It is tough to keep a handle on though...
