Your analysis of schools doesn't seem so far-off for me, and it's not unreasonable to say that not every aspect of social life should be measured by a calculus

Your analysis of schools doesn't seem so far-off for me, and it's not unreasonable to say that not every aspect of social life should be measured by a calculus of upsides to badsides. The utilitarian 'weighing' mode of thinking is not appropriate for every situation, and I think you (inadvertently) made a good case for why, at least with schools. The fact that schools also educate can be worked into an analysis even of the 'bad sides' as not contingent, but a part of the same system that creates the 'bad sides'. The very fact that we consider weighing the 'upsides' of something is if we give it, or part of it, legitimacy in the first place - legitimacy that may not be deserved. I'm silent on the topic of social media, but we wouldn't even begin to consider the 'upside' of murder or rape or defamation, for instance - and that's not because people in the past have done that analysis for us, it's because collective experience has shown the analysis isn't worth doing - that the utilitarian analysis is the wrong method to apply to the question, just as there are good and bad methods in science or philosophy.