That's the thing, must have skipped Nanao, Soul Society was never really explored. Far as I can tell the bulk of the shinigami was supposed to be picked up from the outside where the souls wander and I don't recall they were supposed to live real lives there either. They are souls after all not soulhumans.
While it is left a bit murky, there are definitely Shinigami families. The noble houses (Kuchiki, Shihouin,
Shiba
Well, not Shiba, poor Kaien and his wife got killed before that, but they could've and that they were a noble family implies they are generational like the other noble families