How important are classifications (ACM, AMS, PACS...)?
From the ACM page "How to use the Computing Classification System":


  An important aspect of preparing your paper for publication by ACM
  Press is to provide the proper indexing and retrieval information from
  the ACM Computing Classification System (CCS). This is beneficial to
  you because accurate categorization provides the reader with quick
  content reference, facilitating the search for related literature, as
  well as searches for your work in ACM’s Digital Library and on other
  online resources. It also ensures correct placement when a review
  appears in Computing Reviews.


There's similar verbiage for the AMS MSC. 

In other words, the institution needs it for their own databases and search mechanisms. The AMS probably needs it for something similar. So your use for the classification system depends on how much you expect people to search for your work using the classification structure provided by the institution. For math, I'd expect it to be used a lot: for CS, not so much.