My state provides a webpage for verifying the status of your ballot by serial number. There may also be a way to do so by phone. I’m not aware of a way to obtain the map of ID to voter but I don’t think it’s necessary. Plus it’s radioactive from a voter intimidation and privacy perspective.

> Let's say voter fraud is indeed very low in the US, why not make obvious moves to make it even more accurate and honest?

Because if you aren’t careful you can make it worse.