If the audience cannot enter into the problem, then its value as a tool is diminished.
Case studies are also fraught with peril, but the analysis of where the particulars end and the general principles begin seems the bulk of the exercise anyway.
More than that, they reduce too much of the problem away. It reminds me of the two capacitor paradox [1] which (spoiler alert) only arises because that configuration isn't actually possible to realize in terms of ideal circuit elements.
In particular, we spend a lot of time thinking about what would have to be, in most formulations of the problem, a quickly-decided act (otherwise, why not simply untie the people?) and we have absolute certainty given us as to the consequences, vs. all the uncertainty in real life. The problem is used to get rid of those elements as distractions, but they're essential features of people's reasoning (and reasoning ability) so they're not so easily discarded.
If the audience cannot enter into the problem, then its value as a tool is diminished.
Case studies are also fraught with peril, but the analysis of where the particulars end and the general principles begin seems the bulk of the exercise anyway.