I like eating mulberries... I also use the trunk of the tree as fence posts when it gets big enough to cut down...
Mulberries are attractive to the song birds, and the leaves are forage to a number of lepidoptera, which... help the songbirds to raise their families...
Good in a number of ways... the only problem is that it isn't a native plant...
Over all... I'd enjoy the tree.
If you opted for removal, what would you replace the tree with?
Sure looks like you need a tree there...
Edit:
Found this... Pros and cons of mulberry... Especially the white mulberry that you have:
https://www.foodforestnursery....