I think the sims' traits affect this very strongly.
Like, many of the premades have the Family-oriented trait, and those sims have a much higher chance of having children through Neighborhood Stories. I've noticed the Goths and Bjergsens always have tons of children in every save for example, and what you said about Kristopher Volkov is the same, he's family-oriented but doesn't have a partner so he can only adopt (and does frequently).
I'm not sure what affects the pet adoptions but it could perhaps be Dog lover/Cat lover?
To me this reflects real life nicely, because I know some families with 4-6 children or more, and some with no children at all.
But, if you want the behavior to be different in your game you can always alter it--
Either by turning the "have children" switch off for a while and only turning it on sometimes, or maybe even modifying the Family-oriented sims in CAS with the fulleditmode cheat so they don't have that trait anymore?
I agree it would be great to have something more detailed than an on/off switch in the future. Like a slider for more specific levels of probability, or maybe a Common/Uncommon/Rare checkbox where we could select for various neighborhood stories events to be common, uncommon or rare for various households.
One thing I've noticed over time is that the system seems to be balanced the best when I'm playing one household and everyone including NPCs is on normal aging.
When I play rotationally with only the active household aging and only occasional aging of NPCs, it does feel like the changes in town happen too often and too randomly-- because Neighborhood Stories is still going at the same rate but aging is much slower. NPCs have way too many things happen to them in each lifestage! And way too many of them die in accidents, because those odds are now much higher than the odds of them dying from old age, etc.
I received a tip from someone else that it might make more sense to have the Neighborhood Stories system enabled only occasionally while playing in rotation, kind of like I was already doing with NPC aging.
