This is a really good, thoughtfully crafted question. I'm also child-free by choice and for me personally I can say I have considered that bigger picture.
Whilst there is something attractive about the big network of adults that you describe, I know from my experience of being an adult within my own extended family that those relationships aren't always rosy or easy.
Even where the wholesome interconnected family network is entirely healthy and functional, so often it seems like the mothers in particular have had to sacrifice so much for the happiness of the wider family. They're doing the lions share of raising the kids, caring for elderly aunts/ uncles/ parents, then when they become grannies they're caring for various grandkids - the hard slog isn't just for a few short years when the kids are small, it seems unrelenting from where I'm sitting!
Obviously I won't dodge those responsibilities entirely (nor would I want to), but I feel like choosing to have kids would be opting into a whole world of pain and stress that I just don't want (I say 'pain' because I imagine I'd love them so much that I'd feel their every upset/ loss/ failure/ heartbreak/ set back more deeply than my own!).
That said I have a disabled sibling whose care I'm involved with and for who I will take on more responsibility in the coming years. So maybe I'd have more bandwidth for motherhood if that wasn't a factor, who knows.
Excellent question though.