In most cases, it's a county agency, not a state one, which handles foster/adoptive children. And the federal government must certainly provide some money, because without them there's no way the state or county agencies could afford to operate practically, period.
The problem, however, indeed is accountability. The federal government willingly allocates funds to help abused children, but that's all it does; the fed leaves it to the state and county childrens' services agencies to organize and police themselves - and these local agencies fail miserably. Spectacularly, even.
No case, in my opinion, illustrates this better than a case which came to light right where I live a couple years ago. Two foster parents, the Gravelles, were allowed by their local county children's services agency to adopt 11 children, some with serious behavioral issues. They adopted so many because it just so happens that you get some money from the county when you adopt kids, and even more money if those kids are classified as "special needs". The Gravelles were overwhelmed (duh) and had too much difficulty devoting enough attention to each child, so they did things like have them sleep in small alarm-rigged cages at night, so they wouldn't wander around and wake their foster parents. A social worker was sent around at intervals, but did not report conditions in the house as abusive. In fact, it took a neighbor, who complained to the county sheriff's office about the smell emanating from the house, to make things happen. The good sheriff visited, and was absolutely appalled. The Gravelles were arrested, charged, convicted, and sentenced to a few years in prison. The social worker who visited but did nothing has had her license suspended for five years and was sentenced to probation. And of course, some serious rule changes were made at the county agency to prevent stuff like this from happening again. Yeah, right.
The local and county governments simply suck when it comes to dealing with abused kids. They suck. No two ways about it. They're either neglectful, as mentioned above, or abusive, as mentioned in the opening post. In point of fact, the only thing the various individual agencies have been able to do well is come up with a standardized child abduction alert system - but even this feat was in no small part the work of a national group, the NCMEC.