Just found out that in a comment to an answer that I commented about 5 hrs ago, there is a typo that clearly reverses the meaning of the sentence (the word "now" was mistyped as "not"). I cannot edit the comment now. Why is that and what can I do? Making a new comment just to correct that seems a little odd in that specific situation.
The timed editing period was designed to allow for those occasional "Oops, I made a typo" moments. After that short period, you don't really want to allow extensive editing without the ability for users to track what edits occurred.
Comments were designed to be a light-weight mechanism. There aren't a whole lot of menus and features wrapped around it. But the ability to edit comments would spur a need to have a full public revision history for comments. We don't store prior comment revisions, just edit in place and increment a counter. The use case you mentioned is pretty rare so the effort and complexity has precluded its implementation.
I can't say the feature will never be added. I already suggested the ability for higher-reputation users to edit comments. That's 95% of the way to allowing user self-edited comments. So, vote up that feature if you want it. If it continues to receive significant support, it might make the to-be-implemented queue.