I think you haven't really grappled with how laws get made.
Copyright is a thing we made up because of "people not liking the idea of other people doing something they don't like". The current specific boundaries are a careful compromise about exactly when we protect "using what I published publicly to make money somehow".
Those boundaries in large part exist because of responses to specific technologies. Before the technologies, people didn't care. After, people got upset and then we changed the laws, or the court rulings that provide detailed meaning to the laws shifted.
As an example, you could look at moral rights, which are another intellectual property right the laws for which came much later than copyright. Or you could look at how intellectual property law around music has shifted in response to recording, and again in response to sampling. Or you could look at copyright for text, which was invented in response to the printing press. And more specifically in response to some people using pioneering technology to profit from other people's creative work.
And we might not need any changes in the law here. The people at OpenAI and elsewhere know they're doing something that could well be illegal. They've been repeatedly sued, and they've chosen to make deals with some data-holders. They wouldn't be paying for published data at all if they knew they were in the clear, but they've chosen to cut many deals with publishers powerful enough to sue. They're hoovering up data anyhow because, like too many startups, they've decided they'll do what they want and see if they can get away with it.