каков is neither rare nor archaic. It's an essential word which cannot be replaced by any other in some cases
I just made an attempt to recall a case when I could possibly use this word, and guess what?
It's either my memory fails me or the word is really very rare.
While it can be found sometimes in written discourse it most certainly isn't something that one can hear in a casual conversation.

An excellent example would be, Каковы ваши намерения? Or, Каковы ваши дальнейшие действия?
Well, yes, but it's still limited to these particular phrases, that are a bit stilted anyway.