From a user perspective, I completely understand this issue, and dealing with the aftermath of importing DWG/DXF files into SketchUp can indeed be a major hassle. What you’re looking for is an alternative import method, not the default SketchUp import feature.
Typically, SketchUp doesn’t allow two lines to overlap on the same level; it will automatically split/slice them and randomly assign a tag to the intersection (a tag from one of the initial two lines), which differs from AutoCAD’s behavior.
I suggest trying this method: Import DWG via TrimBIM import. It might offer a more efficient way to handle your DWG/DXF imports while preserving the tag structure.