My neighbor protected his pomegranate crop with organza bags, including a net over the entire tree - we have voracious squirrels here. Squirrels tore through the tree covering and ripped apart each organza bag! He got no pomegranates. I gave him a few of mine - I think my dogs keep the squirrels out of our yard.
As for mulberries, there was a large tree mulberry tree growing outside of my daughter’s school that spilled out onto the sidewalk and road - I managed to grab a few that were over my car. They were absolutely delicious. The variety I see around here is the “Indian Mulberry” - which grows large and provides a lot of shade in our hot climate.
I was asked when we moved in NOT to plant a jacaranda by my neighbors - the purple flowers in the spring stain the sidewalks - and cars too. I honored their wishes, although my nextdoor neighbor planted one that is now huge - that tree shades my home and his during our searing summer so I am grateful for it. It also produces a lot of debris that covers my driveway and median. I blow it out once a week into the street before the sweeper comes by. Worth the cooling from that tree.
Pick your own mulberries. Well, perhaps having a place that grows and sells mulberries you can try different types and see which would be best for you? Its the only mulberry farm I am aware of!