This actually worked well when I asked Gemini to generate a random color, character by character. I was getting Indigo/Electric Indigo a lot if I just asked for a random color on new sessions.
Actually, asking this multiple times to ChatGPT gives me different UUIDs every time, and it checked with a web search that they are not found in public data.
That's because of tokens (and temperature). You could piece back the tokens to parts of existing tokens in public data. And given enough iterations, GPT will probably start showing noticeable patterns (since it's not actually random).