This seems rather shortsighted, children are a drain, but an asset too. I think one should view them as spinoffs, and of course shareholders will have equity in them.
There was an interesting book about this, The Unincorporated Man. Fellow basically gets put in cryostasis and wakes up in future where everyone is a stock venture like this article. There's some fun ideas in there.
Parents in the story get something like a customary 25-50% of the child's shares at birth.
What? You can't sell stocks of your children?!