My gut feeling is that lately (since Pets maybe), the amount of babies has decreased a lot.
I got so annoyed with not having almost any babies in town, that I went and got Nraas Story Progression. It works like a dream. There'll never be going back for me.
So, I think you made a good choice trying it.
EA's storyprogression made many townie families move away, then replaced them with CAS generated families. I didn't like that. I rather want my existing townies to have a kid or two, than have them move out and add some CAS sims to fill the population. Nraas storyprogression does just that.
The amount of new relationships etc indeed felt a bit overwhelming when starting a new game, but it has slowed down over time when the townies have found their place, so to speak. There are occasional breakups and new relationships, but not so many it would feel "unrealistic". Also note you can choose which notifications are displayed. I chose not to display any career or skill related things (only romantic and moves) and it made the amount a lot more easier to handle.