It is extremely time consuming to have to continually scroll down through the webpage to find the date of the post, before I begin reading the post. In gauging how relevant a post is to my particular problem, I always start with the date.
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Most posts are short and don't extend off the screen. Most searches and lists of questions already have dates that you can refer to before even opening the question.
You have the "asked xx:xx" displayed in the listing of question. That is sufficient I think.
In interesting mode you also have the last activity registered.
Everything is editable here -- so the date is not as important.
We actively suppress "too localized" activity and discussion precisely for this reason, to generate artifacts of (reasonably) lasting value.
While in all fairness, we are a hybrid system, this would be akin to asking Wikipedia to put the date at the top of all their pages.