In a Continuation in Part application, and referring only to those claims from the original application where they, and the specifications they refer to, are remaining unchanged – is there any need to include them in the CIP application?
You include the claims you haven't yet claimed and want to claim. You can't have the same claim word-for-word in more than one patent. It would be double patenting.
If you didn't care about making claims that are fully supported in the parent, you would not file a CIP, but rather a "new" application with no connection to the previous application. A CIP is not magic, anything not supported in the parent is treated as if the application was not any kind of continuation. Some practitioners recommend never filing a CIP.
One case for a CIP is that you want to both file claims that are fully supported in the parent and also want to file claims on something that would be considered "new matter" relative to the parent, and you do not want to file two separate applications. Another case is when you are not sure if something will be deemed fully supported by the parent but want to preserve the argument either way. Add more support in the spec. of the CIP and you are a slam dunk that the claim is supported as of the day the CIP was filed and a hope that, if needed, a court might be convinced that it deserves the priority date of the parent.
In a CIP you can have, for example, a claim 1 that is entirely supported by the specification of the parent, and a different independent claim 4 that is not supported by the parent. It would also be possible that an independent claim 1 is fully supported by the parent, but a dependent claim 2 needs the added material of the CIP. Of course, if an independent claim 4 requires the new material (and therefor the new date), any claim dependent on 4 would likewise need the new material/date.