Hi everyone, i'm a mechanical engineer student from italy!
my physics professor during one of his lectures gave us the exact same demonstration about the different distribution of charges on smaller radius corners that walter lewin gave in the first 4 minutes of his online lecture "8.02x - lect 6 - high-voltage breakdown, lightning, sparks, st-elmo's fire" (you can find it on yt. he eventually told us at the end of the lecture, that the demonstration is fundamentally incorrect, and that there is a profound conceptual assumption (no wrong calculus) we made that is profoundly false.. but he then said that, despite that wrong assumption, that model works pretty well at explaining why that happens.
he then gave us the task to find the wrong assumption we (and you) what would you say about that?