I want this question to have an interesting answer, but everyone knows that if this question ever goes to the courts, ownership will go to the people in charge with the money. The idea that Anthropic may not own Claude Code just because Claude wrote it is wishful thinking.
Best part is, it's likely to have a different answer in every country, who knows what'll happen, not every country implicitly sides with the ones with the most money.
I love that genAI art will not be copyrightable and genAI code will be. The power of the Almighty Dollar at work.
They won't want to own code that is malicious\illegal\used in crime, although it's really weird to me that no one (in LEO) seems to care that, for example, grok generates CSAM, revenge porn, probably other illegal things, so they'll probably get to have their cake and eat it too.
It's not wishful thinking, and ownership isn't a foregone conclusion.
Sure the courts could mint a communist society with a few weird decisions about property rights, but this being the US do you really suppose that's likely?
There's really no legal question of any kind that models aren't people and therefore cannot own property (and also cannot enter into legal contract as would be required to reassign the intellectual property they don't and can't own)
I'm not sure Anthropic would appreciate the liability that ownership would imply.
The work-for-hire doctrine actually supports your intuition more than the AI authorship question does. The reason Anthropic likely owns Claude Code has little to do with whether Claude wrote it and everything to do with the employment contracts of the engineers who directed it. The DMCA takedown question is genuinely interesting though because DMCA requires the claimant to assert copyright ownership in good faith. If a court later found the codebase was predominantly AI-authored and therefore not copyrightable, the 8,000 takedowns could be challenged as bad faith DMCA claims. That is a different and more tractable legal question than the ownership one.