Essays and reports are different things and are used for different circumstances and it seems some are getting confused between the two. In a report, it would be appropriate to use headings. In an academic (I'm thinking of 'essay based subjects' such as law, psychology, politics, etc then you'd rarely have to do a report, the exception would be after carrying out field work and experiments. In an engineering subject then the use of reports would be much more common.
edscdk, not entirely sure why you're being so melodramatic. Also, if the tutor told him to do away with headings then that's what to do. It's the tutor that marks the work so best to please them even if you think (wrongly) that it is wrong. Finally, I would never use bullet points in an essay.