Yeah IMO a good outcome would be that training on data you don’t own or license should require release of the model. Is allowed, doesn’t get you something you exclusively own.

Bonus points if existing rights assignments aren’t enough to count as a grant of permission for AI training.

I don't think there's any precedent for requiring someone to distribute a work they created. That sounds expensive and could easily be a contract violation for other data they did license.

Hmm, it is sort of how patents work. Copyright registration involves giving some sort of the work to the Library of Congress, but I'm not familiar with that part of it.