On the short term, yes. On the longer term (probably only a year or two at this rate) no because these models also allow you to generate entirely new voices. We'll likely see features like describing the voice you want with a prompt and getting several to choose from, remixing existing voices, combining voices and creating voices that are impossible for any human to have. The introduction of other forms of recording and reproduction didn't result in total monocultures, even music which gets a bad rap for all sounding the same only has this problem in the mainstream, scratch the surface and you'll find hundreds of weird new genres and styles.

We could see a future where every commercial is narrated by Attenborough or Freeman but indie creators will be pumping out vast quantities of wild interpretations and new applications of the human voice.