It's draws an interesting question though, at what point, if ever, does an AI system move beyond the scope of a tool and into the scope of an assistant? I don't think we are anywhere near that yet, but it's conceivable that we reach a point where that question needs to be answered.
I mean does it matter? Not like assistants get anything out of patents either. For the most part these days even the inventor pretty rarely gets most of the benefit from patents, they've usually signed it away before they even 'invented' the thing.
If any "inventor" is not listed as such on the patent, then it's another way to invalidate the patent. So while possibly not a benefit to the inventor, definitely good for the assignees to have clarity on the matter.
What would be the point of a program owning a patent? Is it going to charge you royalties for use? Where does that money go? If it gets it’s own bank account, what happens when you run two instances of the same program? Do you split the account in half and then join it when one exits?
The second instance is a totally different entity and does not own the patent or bank account of the first, unless they decide to somehow merge their state-vectors and become a single entity.