I have to agree with the posters who report feelings of powerless pst-birth.
I would say I felt completely eradicated. The pressure put on me to just un-self myself and become mother-of-baby was extraordinary, right down to people just not "seeing" me at times. It was crazy.
I think that you are suggesting that there is proffered by some a "power" of being especially tuned in to the "voice" of the - at this moment- voiceless child.
Now, I would say that all this added together comes to this: women are pressured to lose their "self" when becoming "mother", ie, they are pressured to become "0". In lieu of a personhood or agency, they are offered a "shadow" agency as the temporary proxy of the (voiceless, powerless) child. That is, mother ("0") is now offered some kind of positive presence, but only as the proxy for the child's wishes and demands.
She is offered this role on the - entirely dubious - ground that she is "hormonally", "intuitively", "biologically" tuned in to the voiceless voice, the inexpressible wishes and demands, of the child.
She has been stripped of adult personhood and offered instead the proxy agency/personhood of a child - not an adult. And all this on the grounds that "biologically" she's programmed for this.
We might go further and allege that this substitution of actual adult personhood for proxy and temporary minor personhood is also biologically pre-programmed into women.
But we won't, because it sucks. It's really very sexist, I think.
I honestly think that this is why a lot of us are very cautious about jumping right in there and saying that women are biologically attuned to our children.
However, I do think that that is throwing the baby out with the bath water . Perhaps there is a slight tendency towards this gendered attuning. Who knows? Sadly, not enough men do enough childcare to really say anything definite about that.
Still, I think I would be totally hesitant to call it power. I think it is a weasel power - that leeches power away just as it seemingly bestows it.
My guess is it performs similar twists and turns to saying that women can exercise great power by being smashing cooks and utterly raunchy in the bedroom.