This is actually the most plausible situation I've seen someone present so far - the AI takeover would be caused entirely by humans falling for AI hype, that's hilarious.
I don't think the average human would be stupid enough to give an agent posing as another human access to their entire email inbox. But if an agent creates a fake website for a new AI tool that promises to automatically reply to all of your emails and allow you to be 12.3% more productive if you just give it access to your entire email inbox, millions would sign up!