They likely want to limit it early on. For two decades, people have been able to self-publish music on the internet and no longer need the music industry. For some reason, this never posed a significant threat to their income or control, as the ways consumers discover music remained largely the same. The challenge was more about how self-publishing musicians could find an audience.
Now a new frontier is emerging, a whole new category of music. This could include not only AI-generated music created by humans but also AI systems that allow users to generate their own music ("prompt your next playlist"), collaborative approaches, and potentially fully automated systems. Since these are all novel, it's possible that they will first appear outside the control of the established industry, perhaps through a startup that sees no need to collaborate with the current recording industry. Such a startup could become the alternative gateway through which people discover new music, something that didn't happen for self-publishing musicians before.
If these large companies, including YouTube, Deezer, and others who wish to maintain the current state, establish that AI-generated music, identified by content ID systems that detect short snippets of other works, requires licensing, they may later attempt to sue independent sites that host AI music. These sites might not see the need to search for small pieces that, with enough imagination, could potentially come from existing songs.
When I criticize the approach, I am talking about music that is actually generated. If something cuts together existing music, of course that should be licensed. However, the generators I tested do not create works that are substantially similar to other pieces on a large scale. I suspect, though, that if you examine the similarities down to the level of individual seconds, you can find another song that has a very similar second, regardless of whether you recorded it yourself.