"Common C Interface. "
CCI is more about coding style than anything else.
"I don't think it really works or is very useful. "
It depends. For simple chips (like a PIC or AVR), or chips with very diverse peripheral sets (PIC for example), it is more pain to work through an OEM library that covers a wide range of chips, than to work with the chips in question directly.
But coding through a well defined framework is always a plus as it allows reuse of previously coded pieces -> faster development cycle, better reliability, and lower costs / headache.
More so for more complex chips.