Ironically, one good use for that would be to "exfiltrate" entire AI chats from Gemini/AI Studio as Markdown. Doing this by hand is tiresome and Google is obviously not too eager to make it easier (walled garden).

What for? there's already Gemini CLI (https://github.com/google-gemini/gemini-cli) for that, unless I'm missing some crucial feature not supported by that.