Why is it so?
First, you need a way to distinguish different versions of your CIS where you have changed the details of the offer but not the plan name.
Second, it’s always good to date advertising material so that people can at least sense when it might be stale.
Third, in case of a complaint involving the contents of your CIS, you may need to quickly and easily prove what version was current at a certain date.
Fourth, you’ll never keep track internally of what you have / have had in the market at different times unless each CIS is tied to an issue date.
And should a Critical Information Summary include an Offer Close date?
If an offer is only open for a short time, yes.
You aren’t necessarily required to issue a separate CIS for a special offer based on a current plan. But if you do, or if you make a one-off offer that isn’t based on another plan/CIS, then the closing date should be stated. It’s a key item of info about the offer.