I will never be okay with enabling a third party service to skim my emails wholesale, so IMAP creds is absolutely out. I don't need an Unroll.me going on here.

Suggesting users use rules to forward to your service is a good choice, it allows the user to control what you can see, and it's exactly what the user wants you to see. I personally would be nervous about letting a third party see my flight itineraries, as general opsec, but if someone wanted to do this, I think this is the best way to do so.

Browser extensions are a rough choice because if you want to support many email services, you probably will end up asking to see and modify all browsing data, which is a scary permission to give third parties, and arguably one browsers should stop handing out.

I wouldn't mind running my own apps that read my email somewhere I could monitor what they do and ensure they don't talk to any service but my email service. But you won't see widespread usage with selfhosting, and good luck monetizing it.