I get seeds in many of my mulberries. They are not objectionable at all. Seedlings are a constant issue, though.
Interestingly my morus nigra has 3 seedlings growing with it in its pot. I’m not sure what the seedlings are though. They could easily be seedlings from a number of muberry species or a cross among them. I should probably see if I can I’d them before too late though as if they aren’t interesting in some way I don’t want to stress my nigra by having these share the pot with them.
Scott