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.

Scenario 1 adds more to the national GDP.