Fewer family names over time

I realized in the middle of the night that the total number of family names in the world is decreasing. I am not aware of anyone coming up with any new family names. New personal (first) names, yes, but not family names. It's also clear that some family names are dwindling. In most cultures that I am aware of, children take the family name of just one of their parents. In some cultures, children use their parents' family names to build their own compound family name, but there's a pruning process there as well, as otherwise their family names would get infinitely long. Since some names are disappearing, and no new names are appearing, the net result is fewer names over time.

None of the above seems wrong, but it sure is a weird thought to have.