I mean, technically they can by requesting it. But the reality is that those custom changes only last so long unless you effectively open with them at every session start. And some people do that. Until recent gpt changes, I was largely relying on context and saved 'memories' and keywords, but recent updates made it less reliable again.

I do like the idea of AI personalities ( I actually use them a fair bit for varying opposing perspectives ), but I am not entirely certain people want that.