Chatbot presence restrictions
Chat bots are intended for a channel owner to engage and moderate THEIR chat and channel. It is inappropriate, unwelcome, and absolutely NOT HARMLESS. You would NEVER in your right mind allow some stranger (or their spy cam and mic) to lurk unwelcome in your home.
Chatbots should not have the same account-like status as real people. They should be restricted to their owner's channel and chat completely via implementation. They should not be permitted to roam freely.
Your analogy is wrong: bots aren't invading your home (or if they are, that's a matter for the police) when you are putting on a public performance and the bots are part of that public. If you want to do private shows, there are options for that.
If you have problems with bots spamming your chat, report and ban them. Or ban them even if they aren't. Just be careful not to get too aggressive and accidentally ban real chatters (who also weren't invited).
Imagine if twitch users made a chat bot to post feedback continuously, flooding the feedback with their ideas.