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However, with the rise of living costs, now both partners need a full-time job, and the domestic labor is still there; more work needs to be done than before, despite technology making the individual worker more productive. It's not a surprise that fewer people are able to have children; they have more work and are still just barely paying the bills.
In the 70s, there was a movement called the "International Wages for Housework Campaign," which argued that women should be paid a salary for domestic labor, which is essential to society, and that this is an essential component of Women's Liberation [2]. It's interestingly contrary to the view that feminists are all liberal individualists who don't believe in men and women being different.
I don't see this as a "biology is destiny" issue, I see this as a women are still facing pressures from the past and facing pressures of the present.
I don’t think biology is deterministic, but it is a factor, for both sexes. (Note that surveys show little to no difference between men and women when it comes to the question of whether they want children and how many.) My suggestion is instead that we have a market failure. People have choices, but not necessarily the ones that will make them happy. The solution to market failure is, of course, regulation of the market, but western individualists don’t want to hear that.
That doesn't follow from what they said. Men never had to do the child raising. Men probably do more childraising and housework than they used to do in the past, because they've been sharing domestic labor more as a result of the spread of feminism. OP is saying that the amount of work between a heterosexual couple has risen: before, it was the man doing a full-time salaried job, and the woman doing housework, cooking, shopping, and childraising as her full-time, unpaid job; and now they're both working full-time, and they have to split the domestic labor between them somehow, or, it's all on the woman and the man does no more than he used to do.
This is a bit oversimplified, though. There were always working-class women who worked as maids or in shops, or, in the 20th century, as teachers and secretaries. Those lower-class women just weren't paid that much. They always had a "second shift" [1], but since the 60s, it's spread to all women.