Copyright isn't about storing copies. It's about making copies.
How do you think the AI companies extract all the statistical info about some content?
Spoiler: They copy that copyright protected work onto their machines where they do the data analysis.
At this point copyright was already violated. They usually never had the right to make copies for the purpose to extract statistics about it in the first place. "Because it's on the internet" doesn't give you such a license.
The current LLM "AI" only exists on the grounds of massive copyright volitions. It's the exact same situation as with Napster in the past.
No mater how often MS and friends hallucinate something about "fair use", it is not, and the only realistic legal outcome in the long run will be the same as for Napster: AI training is piracy. On a global "internet scale". (The only sad thing is likely nobody of the directly involved will end up in jail, like they do e.g. with people sharing torrents).