As the author of the post who likely initiated this one, I would like to chip in. Jonas is known for very well-written and thought-out posts. In my reply I will simply list thoughts that come to my mind, which aren't necessarily related to one another:
Obviously, there is the counter position, and correct observation, that someone wrongly accused might carry a stigma even if justly exonerated. But in my eyes, the above outweighs this drawback: how often will that happen? Who would make such a mad claim if it isn't 99% certain?
(2) Who is the plagiarizer? If a 135 rep user decides to make a post which consists of having copied one each by BMS and AN, with some MathOverflow thrown in, it strikes me as easily handled and, to an extent, as humorous. If the third highest reputation gainer of the month has a long history of plagiarizing, it strikes me as very worrisome, and worthy of public debate to elicit feedback.
(3) Value of going public: Had this not gone public, it is almost certain that not all cases that are outlined in EN's answer would have become known. The final feedback to my claim of plagiarism is 'not proven as there is some debate.' After I submitted my post containing the sentence "Assume next that it holds for some generic n. You need to show that then it also holds for n+1. As it holds for n, you can assume that", other user user posted 5 minutes after me, with changed indices - but the same bracket missing in the same spot - an addition to his post starting with "Assume next that it holds for some generic k. You need to show that then it also holds for k+1. As it holds for k, you can assume that" (emphasis added). By this standard, there are several German ministers who would still be in office as opposed to enjoying salary increases from now being in industry. I tried to avoid pointing to this as I have already stepped on too many toes, but I can only scratch my head. One of my favorite users here keeps chipping in implying that nothing has been proven, while rather clearly defending other user, for reasons I honestly do not understand.
So it is good that the other cases which might not have come public, actually did, because had I only flagged my post, and had my claim only been evaluated based on its own merits, it would apparently have been declined (this is assuming that moderators would not have found the other cases, which obviously is not clear - in fact, I am sure some would have been found. Still.).
(4) Burden on the moderators: The particular case was clearly eased by allowing others to do their own digging, and chipping in. The moderators do a great, and burdensome job - and probably will reply that they don't mind, that this is due process, and they volunteered to it, which is true. But relying on a community to chip in, in this particular case, reduces some of their burden, and speeds the process up. Edit/addendum: It is also easier for other users who might have experienced it first-hand to remember such cases because what happened might be buried in edit history (at least one of the cases reported was only visible, I believe, when unrolling such history), which would mean that a moderator, obviously, not originally involved would not only have to compare posts, but posts as edited over time.