How can I send a cc: of an Activity assignment e-mail to another user, as an FYI?
Functionally I am always confused about FYI mail. What is it supposed to do? As a receiver I am not supposed to do anything but I am supposed to read it just in case? I tend to just delete them if I can not identify any action, and I also tend to say so.

I assume you want to send the FYI email to a certain relationship contact (manager or something like that) and you have set up the relations in such a way? 

If that is the case you might have a play with the CiviRules extension (read the blog at https://civicrm.org/blogs/erikhommel/extension-civirules-now-avaible-download-live-showcase-maf-norge for some background). 

CiviRules allows you to setup specific actions (like sending a mail) based on a trigger (activity changed for example) checked against certain conditions (activity type is send email). 

You will also need the Send Email API extension, can be found here https://civicrm.org/extensions/e-mail-api. I think this can help you to set up what you want, although you might have to develop (or get someone to develop for you) an additional condition.