Publicly displayed status symbols tend to lead to egotism and elitism even in the most relaxed communities. Hell, even things that don't seem like they would be status symbols end up being used as such if they're displayed in public and create different classes of people. Personal customization things, like our usernames and avatars and the status messages beneath them, don't tend to cause this effect thanks to the fact that they can be changed on a whim and do not set up a separation of classes of people.
For an Iwaku-specific example of this in action, pay attention to anyone who specifically refers to someone as a blue star or red star, which of course references the colored star near each person's avatar that indicates whether they are adults or not. It's not a common thing, but I have seem some instances of elitism where a person will talk down about "blue stars" as a group of people. It's a manifestation of age-based bias rather than pure status elitism of course, but it's still something those prone to elitist mindsets can grab on to and use to set themselves and their fellows up as better than the other group. On the other hand, there are also people who refer to "blue stars" in a non-negative light, but those with a blue star often feel like they're being singled out or targeted in some negative way nonetheless. This sort of group forming and group conflict mentality is a natural part of human psychology, happens all the time for nonsensical things, and it's best to minimize them when possible.
Displaying post counts would lead to elitism in the form of people saying things like "they only have X posts, they're new here, their opinion doesn't matter" or "lol you only have X posts? get on my level." It's a thing I noticed happening back when post counts were publicly displayed here on Iwaku. It's a thing that happens on every forum with public post counts. It's a part of human nature to look for those exhibiting similar characteristics, then to build a group mentality around it and act differently toward those from other groups.
Publicly displaying trophies would cause this, and for that reason I think they should remain a private thing tucked away where a lot of people apparently can't even find out how to view them. That's the perfect place for trophies that don't truly mean anything and would only cause strife and division if they were displayed in public.