It seems like the government's willingness to spend money or create inconveniences in order to learn more about overstays has been pretty limited, and also that they care a lot more about overstays from poor countries than from rich countries. (I think some people in Congress are really upset about it, but it just doesn't look like the immigration authorities cares that much compared to the controls at the borders and ports of entry.)

Also, some incidents of investigating and attempting to deport overstays who were deeply integrated into communities and clearly doing super-productive things have led to bad PR for immigration authorities, which could be another reason those authorities are incentivized not to get too good at it (though influenced by factors like what part of the country, where the people have migrated from, what their socioeconomic status is, and others).