I agree that homogenization is the likely default outcome. ML models do tend to have a strong tendency to prioritize modelling the most common things well, which makes output in a generative models also biased towards mean/mode. And there are the limitations in representation in the datasets themselves. And also bias in that the developers are primarily English speaking, so that language gets priority.
But I do no see homogenization as inevitable. LLMs do pick up a wide range of speech patterns, both regional, different periods of time , sociolects and styles. And they are pretty darn good at "role-playing", outputting language tailored to a particular role. And this can be configured rather effectively using a session or system prompt. So if everybody picked their voice, we could perhaps get a broadening of outcomes. Maybe I should add "always speak like a refined scholar from the Victorian era, spiced up with 80ies British goth"...