Your question (by your own explanatory statements) is not related to the scope or content of comments but only seeks to simplify the steps / effort required to edit a comment after the expiry of 5 minutes. I have experienced exactly what you described in terms of editing a comment and finding that 5 minutes has elapsed, therefore having to copy and paste the edit as a new comment and delete the earlier comment to clean up. It is only slightly laborious, IMHO, but I can understand that your suggestion is meant to smoothen the 'flow' of the user experience.
I am sure you are aware that we can delete any of our own comments at any time, which by itself is sufficient to throw confusion upon the comments that follow. Deleting a comment which was in the middle of a 'discussion / debate' can create as much confusion as editing it. Hence I don't think there is any real reason for specially allowing the editing of the last comment alone, after a specified time period. If editing is to be allowed beyond 5 minutes, then editing all comments could be permitted without setting any time limit.
Why then did the democratic process at StackExchange in all its collective wisdom set such a limit on editing comments? The senior member has already set out the major reasons in the earlier answer, of which I am mainly convinced by the following (theoretical) point:
And theoretically, this goes against the whole raison d'etre of Stack Exchange. Comments are for pointing out something relevant or for asking for clarification of the question; they are absolutely not for 'contributing to the debate'.
-- TimLymington (extract; see earlier answer for details)
I also infer (again as stated in the earlier answer) that we are meant to edit the comments only to remove typographic errors, or clarify the point, and not to substantially change the content. If 5 minutes have passed after commenting, we shall have no choice but to delete and re-comment. IT WOULD SEEM that StackExchange is telling us, think before you comment! Even if unintended, it is an effective way of discouraging impulsive and possibly inflammatory comments, especially on sensitive issues.
Now I shall try to consider a few other, practical problems with actually allowing the editing of 'the last comment' after 5 minutes:
(1) this is possibly the most serious: simply editing the last comment after a few hours without fresh responses may provoke a fresh round of discussion / debate, which is not the intended purpose of comments, as already highlighted in the previous answer.
(2) if the last comment was rather contentious, or very interesting, or even simply if someone woke up 6 hours later in a different time zone, somebody might well be composing a delayed response even as you are busily editing your 'last comment'. Now, if that response is posted a fraction earlier, your edit will be automatically denied because yours is no longer the last comment, as has been noted in the earlier answer. (On the other hand...)
(3) if that 'delayed response' to your last comment happens to be posted just after your edit was allowed, then there is a good chance that much confusion will ensue because somebody responded to something in your comment that you (unknowingly) changed by editing it a moment before they (unknowingly) posted their comment!
In either case, the purpose will not be served. And what if some sort of entirely avoidable chain reaction of comments were to occur over such a misunderstanding? I have actually seen that happen here over some controversial topics. That is exactly why no more 'contesting the ball' is allowed in rugby union after the referee has blown the whistle.
So I hope you will understand why it was left simple as we do it now!