A lot of the US road map was imported from TIGER (<https://en.wikipedia.org/wiki/Topologically_Integrated_Geogr...>). This is an electronic mapping system set up in the 90s by the US Government to aid in conducting the census. The TIGER data doesn’t have any address information at all, just road shapes. No information about the type of road, the number of lanes, the quality of the surface, presence of sidewalks, signals at intersections, anything. Just the paths the roads follow, and those paths are often of extremely poor quality. The resulting OSM maps are barely usable; sometimes they are not even recognizable by locals.
So OSM has decent geographical coverage of the US, but relies very heavily on individual contributors to correct the deficiencies and add useful information to the maps. The only way it will be usable for you is if others have improved it. The only way it will be usable for others is if you jump back in and do the same.
> 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
So OSM has decent geographical coverage of the US, but relies very heavily on individual contributors to correct the deficiencies and add useful information to the maps. The only way it will be usable for you is if others have improved it. The only way it will be usable for others is if you jump back in and do the same.