The "Where is the shared social cost ^ here" question?
marriage
This is a temporary contract which can be terminated by either living party or by the death of one. There is no legal obligation on the womans spouse to provide financially with in the marriage. She and her child could be starvimg to death on the side of road and the States starting point is a DNA test and half the cost of feeding and housing any child [(edit) is still the responsibility of the mother]
She can be disinherit via her spouses will.
If disinherit or divorced she needs to be able to afford to go to the courts and argue a legal case that her life and non-financial contributions within her marriage were sufficient to allow the courts to transfer some of her spouses personal property (assets) to her.
You have argued that her contributions have no economic value. If that is true she gets no rights to access any accumulated wealth of her spouse.
by working part time
This at a financial cost she needs to be able to pay for child care before she can free up time work.
choosing a route back into employment at the appropriate time
Again this is at a financial cost. Some of this cost may be covered by public funds by paying a childminder or teacher but regular employment hours are not designed around raising a replacement worker.
It hugely raises the incentive on women not to go back to work. That may work beautifully for families in certain instances (and why not do it if the economics works) but it doesn't help the broader problem that women face in the workplace. It deepens the already strong tendency of employers to believe that a woman with children is less reliable, less hardworking and more likely to drop out of work. That would not benefit the large numbers of mothers who want to work.
You keep using the word work and reward.
Is the childminder (a stranger to the child) rewarded or paid?
Is the teacher (a stranger to the child) rewarded or paid?
If a mother is doing the same work why is it a reward not a payment for the time invested?
At the end of 9 months + 18 years society ends up with the finished product. A human who may or may not be a benificial contributor to society.
Someone has to do the work as children dont raise themselves.
Yet when it comes to recognising that raising a child is work Western society is not willing to see a mother as a worker role or as having engaged in work at all.