Distilling is only prohibited from chats you prompt. But there are lots in the open like the LMSYS Chatbot Arena data. It's a essentially one of the largest public sources of preference data, maybe still useful for boostraping RLHF and successor techniques (possibly a more highly educated contributor base than the low paid contractors), and was full of GPT-4-era inputs.
How is distilling prohibited? AFAIK, the input is mine, and the output is not copyrightable.