Here in my locale I've found more food for birds results in more birds. I thought once I planted blackberries here at the house, the birds would slow down pecking peaches. But bird pecks increased.
As the blackerries started to produce, the birds ate them all. I thought once the berries ramped up production, the birds wouldn't be able to eat them all, but they called more in to help with the task.
I've found, if I net everything early on, the birds figure out there isn't any food and aren't as much of a problem as the season progresses.
Wild mulberries are a mixed bag for fresh eating. Some can be sweet, others are pretty bland. They all tend to be pretty small.