Why would Microsoft use the standard Microsoft Windows dialogs...?
...or menus, or toolbars, or even edit controls. In a normal "Open file" dialog box you can right-click the edit box and paste the filename. In Office, you can't. (You can still paste by Ctrl+V though).
It may be because some Office apps were initially designed outside of MS, but if that was the case, they've had more than enough time to standardize. Maybe MS thinks Office should behave and look slightly different from the rest of Windows, so that people know what they paid for, who knows. Certainly in the case of common controls there is less functionality in Office than in the OS itself.
As for the OP question: for those dialogs where Ctrl+C does not work, would it help to make a screenshot and paste it into Evernote or maybe OneNote? Can these apps OCR such a screenshot well enough? (It's probably faster to just type the text yourself most of the time anyway.)