The primary use in closing a question is that it prevents new answers from being submitted. Usually this is used to prevent a challenge from accumulating answers while their issues are being sorted out.
If we want to prevent KOTHs from accumulating answers after their deadlines then closing them is a good way to do this.
However the question stands as to whether or not we want to stop new answers from being posted. You make a case for them in your question.
And I agree with this case I do think that there is value in new answers to old questions. However currently we disallow answers that make no attempt to optimize for the challenge. Answers submitted after the deadline cannot win or even place and thus do not optimize for the challenge. In fact in a sense it is not even possible to do worse than a late answer. And so by our current consensus they are disallowed. (there are no "non-competing" answers)
So what can we do about these valuable contributions that are being lost because a challenge is closed to submissions? Well I am of the belief that if you think you have a valuable contribution then you should re-ask the challenge, hopefully improve it, perhaps remove the deadline, so that your new answer can compete against other answers. It may be a good idea in these cases to move over some of the existing answers as community wikis. Valuable contributions go to waste if they can not actually compete. They are already locked out of the challenge whether we prevent them from being posted or not.
In this case it is useful to close the challenges. This will prevent invalid answers and will make room for new versions of the challenge.
This is a little different for answer-chaining questions since starting the question anew radically changes things and a contribution to an old question does not necessarily work for a new one. This situation is discussed more thoroughly here. I think we should stick with what is said there, but I don't want to give the impression that my answer applies to answer chaining questions.
This is Sriotchilism O'Zaic's answer originally, I am reposting under CW as they wish to be disassociated from it