That's a great idea. Free databases are limited to 10,000 rows so they are likely to be very small in most cases, would totally fit in an email attachment.

Email is not actually private in many instances, so this might be an unworkable solution, possibly even a legal minefield too.

Maybe encrypt the email attachment with an encryption key that is only accessible behind Heroku's 2-factor login page? Problem is, it would probably still reveal basic metadata and database sizes.