I came across this interesting video that shows just that. I think from a lot of locations, this would block the southern sky along the ecliptic making it hard to view the planets or a lot of other good stuff to the south. Then again, the light pollution from this would be miserable too.
But then again, everything is so perfectly balanced to have life on this planet that if a moon broke up like that at one time, maybe we never would have evolved in the first place?
Of course we already have a ring around Earth that we made ourselves!