To me, moss is not just more organic material, but really high quality organic material! ...but I don't live in a place where moss can easily grow in a garden bed.

I suspect it's going to vary based on area, but living where it's dry, I like to bury as much moisture as I can in the base of my beds.

For me, the point of the decaying organic material is to help my mineral soil hold water and absorb nutrients more effectively, so having it damp before I bury it is a benefit.

I think we made the mistake of using black walnut in a bed. It has chemicals that basically kills other plants.

As for moss, sure why not? More organic matter. Unless you want to use it elsewhere for more decoration purposes