US Supreme Court rules for Google over Oracle

No, assigning copyright to somebody else is not necessary by any means. There are jurisdictions (Germany for instance) where that simply is not possible. I create a work, I (or the company employing me for that purpose) hold the copyright; after I die, my heirs do. End of story.

So what happens instead? I sell an exclusive and perpetual license to exercise those rights to somebody else. Same effect as a copyright transfer but an entirely different legal theory behind it, which matters a lot e.g. when the work is translated to a new medium that didn't exist when the sale took place. Lawyers tend to have a lot of fun trying to guess the intent behind those contracts.