To be clear, women’s work before World War II was more than just the dishes. If you look at the guidebooks published for housewives back then, you’ll see that they were expected to have quite a few skills that most households now generally outsourc to external businesses:

• Feeding the family. This was more than just cooking. They were expected to process foods from a much less processed state (much more butchery of meats and cleaning and processing of vegetable products, dairy products, baked goods), and then preserve foods for out-of-season consumption (pickling, preserving in jams/jellies, home canning, drying, and in some cultures smoking). Much of this work is now done by the industrial food processing industry so that we can buy cans or jars or boxes of the stuff that’s already processed or partially processed. Even our fresh foods have been cleaned and sorted and trimmed to mainly just the edible parts.
• Making and maintaining textiles. We see bits of this surviving into knitting and crocheting as hobbies, but back before the rise of cheap apparel it was important to be able to clean and repair clothes that we’d now just take to our local dry cleaner.
• Maintaining the house itself. Home improvement is masculine coded today, but a lot of the stuff that qualifies as home maintenance was traditionally the work of a homemaker. Plus things like heating the house required active involvement of keeping fires burning and fuel on hand.
• Making household consumables. Homemakers were making their own soap, their own candles, and all sorts of little tools.

The economic shifts that come from women leaving the home for the paid workforce are all over, and some of them are pretty pronounced. But it’s important to remember that women worked hard before they ever got paid for it. Life was toil.

It’s not actually a clear inverse relationship on the individual level, even if the data shows a correlation at the national level.

There are a few things happening that complicate the analysis at the individual level, too:

• Wealth/income are correlated with age, and 40 year olds tend to have both higher incomes and lower fertility rates than 25 year olds.
• Wealth also correlates with race, for better or for worse, and there have always been persistent differences in birth rates by race.
• The sample sizes aren’t big enough to show whether the very rich (95th+ percentile) actually reverse the trend, to where being richer is correlated with higher birth rates, where the curve ticks back upward at very high incomes.
• The correlation is actually the other direction when looking at the individual incomes in certain countries (Netherlands, Sweden, Norway), and the effect is stronger when looking at men and their incomes.

Other country level data also suggest that there are big cultural factors in birth rates as well.

All in all, the relationship between income and fertility is complicated, with lots of other factors at play.