there's only ~3300 counties in the USA.
i'll let you extrapolate how CPS can handle "4000/day". Like, 800 people with my wife's qualifications and caseload is equivalent to 4000/day. there's ~5000 caseworkers in the US per statistia:
> In 2022, there were about 5,036 intake and screening workers in child protective services in the United States. In total, there were about 30,750 people working in child protective services in that year.