I just don't think things are that easy nonnanna although I do somewhat agree with your aim.
For instance, if we had another "great global recession" (heaven forbid) you would have a real downturn in births and difficulty later on in rebuilding the economy. We need the closest to a steady birth-rate as we can get to keep the country in balance.
My solution would be that all child benefits are withdrawn and a wrap around child care system set up which anyone with a child could use. So there would be 24/7 nursery and pre-school care which you could use for the hours you needed (even overnight and weekends). You would then be able to take any job available and use the hours you needed. This could be used by all, so a high paid worker sent abroad, say, for a few days, could use this.
This care system would continue during the school years - but please, not with the expectation that it would be provided by teachers - giving breakfast clubs, after-school and homework clubs, and boarding facilities.
The drawback with this is that only those who can afford to work fewer hours because of higher income coming into the home or a willingness to forgo some years of income because you could otherwise support your family (another worker) would be able to be at home. However, until we started giving benefits because someone was in a single adult family it was ever thus. The idea that everyone lived the 1950s picture-book life with the children coming home to a sparkling house with the new fridge and Television - and lashings of ginger beer - was never true. Mum's, aunts and sisters helped one another and people worked part time; many people had to work who now feel a right, because of a child, not to.
This may seem harsh but we are condemning many women to no work, no possibility of improving their place on the career ladder and a very poor retirement so I believe it is best for them and, ultimately for their children to enable them to work. However, if we do we must have a support system in place to make it possible.