> TIGER data doesn’t have any address information at all
In the EDGE tables it does have ZIP codes and house number ranges, split into left and right side of the road. ZIP codes were imported into OpenStreetMap data. House number ranges are imported into the OpenStreetMap search into a separate database table, so searching works in a lot of areas but it's far from complete, all the issues you mentioned with roads that don't even exist etc
In the EDGE tables it does have ZIP codes and house number ranges, split into left and right side of the road. ZIP codes were imported into OpenStreetMap data. House number ranges are imported into the OpenStreetMap search into a separate database table, so searching works in a lot of areas but it's far from complete, all the issues you mentioned with roads that don't even exist etc