I have done BOM where the fabric was provided, but since each of us put our together differently, they did not all look alike. In fact, it was educational to see how a different setting made each one very different.
And I have done BOM where we all make exactly the same blocks, but we did our own fabric choices. That was a big WOW for me. Sometimes the blocks didn't even look alike because maybe someone used very popping colors, or muted colors.
Both kinds of BOMs were extremely helpful to me, and ended up being beautiful quilts. The fabric provided quilts weren't always to my taste, but there was always someone in my family who wanted them.