I agree with you - if you need to pay someone a full time wage to go out and earn a full time wage, the sum will be nearly zero. The same issue applies for long term care facilities where a team of multiple specialized providers is needed to care for someone around the clock. The assumption that care should be cheap implies that care work is less valuable than whatever the worker themself does.

Much like mail delivery, daycare and elder care would be better as publicly funded services. They can’t necessarily turn a profit, but still need to exist for the betterment of society