After a discussion with an MSE user about this, I have concluded that the cutoff dates, if they should be there at all, should not be part of the title. Perhaps they could be boxed/bolded next to the tags of the question.
Regarding their existence, I think that people should have the choice. For example, some people may like the idea of MathCh.SE posts, in a way, resembling competition-like scenarios, just like in international challenges. However, to compromise, this does not have to mean that users cannot answer after the deadline, as a community-wiki answer could be implemented instead. It would simply mean that you wouldn't be given any rep for upvotes on the answer.
StackExchange questions are intended to last forever - would the end date be simply when the best answer would be accepted?
Whilst I agree on the first part, for SE, answers can still be posted after an older answer has been accepted. There have been many cases where askers give the green tick to that new answer.