I'd assume that this is more likely true in countries mostly populated by recent immigrants.

Whether family names are more differentiated depends on where you live.

The USA has a wide variety, but there are also places like Vietnam where only a handful of family names are in common use and more than 30% of people are Nguyens.

I think that makes sense both from an organizational and cultural perspective. Context usually supplies whatever information is needed for personal names so less disambiguation is required, and they are used much more so some simplicity is useful/natural consequence of human nature. Family names are used less frequently and with less context and frankly is how people distinguish their group from others. So yeah, think it checks out.