"The only interesting thing it does (apart from storing constants like its serial number and variables like your phone book and text messages) is to generate authentication responses"

The most interesting thing your SIM card does is run arbitrary programs that can be uploaded to them, without your knowledge, by the carrier:

https://www.defcon.org/images/defcon-21/dc-21-presentations/...

The SIM card is a full computer, with its own CPU and memory, that lives inside your phone and that you have no control over.