It sounds like these agencies are in the (very lucrative) business of representing only the side that pays. Seems like an obvious conflict of interest in terms of finding the best match. Is that why they waste so much time sending out low level nannies who will take any job they can get?
I'm not sure where the conflict of interest is. The agencies are in the business of finding qualified nannies for families, who pay for that service. They are not in the business of creating mutually beneficial matches, necessarily, because they work for the parents. Sure, it's good for everyone when they *do* make mutually beneficial matches, but that isn't the goal of the agency. They find nannies for families. The nannies don't have the power in the equation. There are many nannies for every job, at a wide range of "acceptable" wages and benefits, and there is little to motivate agencies to consider their needs over the paying family. (I'm not endorsing this situation, btw.)
Of course, the equation changes if you are a relief nanny or a specialized night or baby nurse. In that case, the family needs the nanny more than she needs them and would be more likely to submit to background checks and the like.
As for creepy DBs, well, I don't know that a background check would help much there.
I think Nannydeb has good advice on including language in the contract that insures the family pays on time or faces penalties.