In the example provided of leaking a private video, you already need access to the private video to even comment on it. That scenario is not much of an exploit.
Unless there's a better example of what can be abused, the more realistic concern is authority laundering where a command tricks YouTube into giving the user instructions that sound like they're coming from Google. Another risk is using it to get the AI to misrepresent the results of its task.
I think the comment can be left on any video on the channel?