I'm curious to what you think could be made illegal.
Expanding copyright or trademark laws to include voices would be close to impossible. It's the same with particular styles of art: it can't be done.
Copyright already protects a combination of things that make a character or trademarked entity unique, however with provisions for Fair Use, derivative art, commentary and parody. Fair Use has come into play in most court cases since the late 90's, where Disney (porn), Dallas Cowboys (Cheerleader porn parodies), and many others have lost... while Hustler (parody & social commentary), Google (Fair Use of data for book scraping) have won.
When it comes to deep-fakes of actual people, identity theft and dignity protection laws (EU) already have this covered. Although it rarely ever goes to court, because most (all?) of the infractions are underground i.e. forums like these or private discord servers. Deep-fakes are older than than the Internet itself.
Private companies on the other hand, like YouTube, Twitter, PayPal or MastCard/Visa, Midjourney, Stable Diffusion (official) may ban certain activities whenever and for whatever reason they want to. Or are told to by investors, advertisers, and/or governmental persuasion.
I expect a lot of complaining, hair-pulling, and rage protests, but whether actual laws get changed, I doubt it.
But being "underground" is gonna be a wild ride for sure, and I can't wait for it!