There's never a good reason to berate anyone publicly, particularly online, where there is much less opportunity to fine-tune the message so that it is understood and remains at the appropriate level.
Which is more toxic to an online community? Is it the people who are ignorant of the guidelines (or who choose to disregard them)? Or is it self-appointed enforcers of orthodoxy who berate breaches of etiquette?
More to the specific point, should anyone care about public accusations of cheating? I suppose it's common to wonder whether one's loss is the result of collusion, but most of the time it's not.
My hypothesis is that someone sophisticated enough to detect actual cheating already knows that accusations should be made privately. Therefore, public accusations are made predominantly by those who would not be able to discern actual cheating.
Is there some effect of being accused publicly? I argue that if there is one, it's a positive one! Based on the preceding point, only unsophisticated players would pay any attention to public accusations. Is it a bad thing if unsophisticated players shy away from you? Maybe so if your goal is easy points, less so if you want good games.