As far as I know, the only thread-category that this restriction applies to is “Conversation” (as opposed to “Conversation Side-conversation”, etc).
Unfortunately this is by far the most common thread category used on this forum. It tends to be used as the default, even where its public-facing aspect is clearly not needed (such as in this topic), often slowing down non-controversial conversations. Are these categories hard-wired by the forum software, or can they be added to? Does anybody know?
I think that the delay you allude to may be exacerbated by the fact that most (all?) moderators appear to be from US time-zones, and so are active at roughly the same times.