I don't mind them myself. I kinda like looking at other peoples' post counts. I like to see it not as a measure of who's "better" but rather a measure of general activity.
Yeah, same, but with the drama they've caused recently, it seems like not everyone's mature enough for that.
In all my years here I must say I've seen very little drama caused by post counts. I do remember the ooooold karma system we used to have which did cause a bit of legitimate trouble.
And again, I agree that a post count isn't really a massively important thing, but it's still considered a standard feature of many forums and generally just something I find to be a "nice to have". Not for competition regarding who can post the most but rather for your own personal enjoyment, like, "Oh wow, I've got over 3200 posts here!" - and then that's a number I've acquired throughout my years of contributing to the forum rather than being an overly active member that just kept posting for the sake of increasing a number.
What I'm saying is, I don't think too much about the post counts but it would perhaps be a bit of a shame to remove that since it's such a basic feature for any forum to have. Rather - try and discourage competition and inflation of one's post count. There's already a rule that prohibits spamming and discussions that go overly off topic which could be attributed to posts where the sole purpose is to inflate your post count and also several high-traffic boards where your posts do not contribute to your overall post count.
And really, whilst a post count is the feature that's in the center of this issue - the users making it a problem is the ones actually causing the issue. Thus I think you should keep looking over the troublemakers and make it clear that such behavior shouldn't be encouraged on this forum, referencing the aforementioned no-spam rule as well as the no-drama rule as opposed to resorting to removing something as basic as a post count.
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Also, just for curiosity; Which thread is it that was moved? I haven't stayed too up to date with some of the newer threads floating around lately.