if you hired care assistant then you have time for some other activities like work which is more profitable than cost of care assistant thus economy has more goods. Life expectancy lowers when young people die, most often in work accidents which is related to low unemployment.
You're completely missing the problem. The care assistant, being a fungible and commoditized service provider, can never provide the kinds of illiquid unmeasurable goods that are generated by long-term and durable relationships.
My wife had a good job. She made the median household income in the area on her salary alone (my salary was still better, but that's beside the point).
When we had our second kid, the hustle wasn't worth it. Two kids in daycare took 90% of her take home pay. It was costing us more for her to work than to stay home with the kids.
Also, kids need their parents. An infant being away from their mom for that long is unhealthy for the infant
It's a choice, economy is about choices and math (staying at home cost < cost of kindergarten) is the tool. (in EU you may prefer to go to work because additional income is that time is added to retirement, even if money is low it has some value).
Your argument hinges on my work being more profitable than a care assistants. While that's maybe true, the difference showing in GDP is not the difference of profitability or "value" in our work. What if I'm a care assistant myself? Imagine two care assistants and two scenarios:
1. They are working from Monday to Saturday. They can't take Saturday off, so they hire a care assistant to take care of their grandma on Saturdays, they happen to hire each other.
2. They are working from Monday to Friday. They take care of their own grandma over the weekends.
