It's not impossible to solve, just that doing so may necessitate compromising anonymity. Just require users (humans, bots, AI agents, ...) to provide a secure ID of some sort. For a human it could just be something that you applied for once and is installed on your PC/phone, accessible to the browser.

Of course people can fake it, just as they fake other kinds of ID, but it would at least mean that officially sanctioned agents from OpenAI/etc would need to identify themselves.