That makes a lot of sense! On the backend, we've already built a way to view content samples (for compliance reasons, e.g. if something looks spammy and we need a human to confirm). It would certainly be possible to expose that functionality to users. I'll run that by the PM on the relevant team - you're not alone in wanting that feature.
You can look in the Email Activity tab to see a history of events, along with their category (you might use this for "receipt", "forgot password", etc.).