You can improve things with prompting but can also fine tune them to be completely human. The fun part is it doesn't just apply to text, you can also do it with Image Gen like Boring Reality (https://civitai.com/models/310571/boring-reality) (Warning: there is a lot of NSFW content on Civit if you click around).
My pet theory is the BigCo's are walking a tightrope of model safety and are intentionally incorporating some uncanny valley into their products, since if people really knew that AI could "talk like Pete" they would get uneasy. The cognitive dissonance doesn't kick in when a bot talks like a drone from HR instead of a real person.