It would be considered "the right thing" to do something that's so common you probably want it without asking. I don't think CADR would check for NIL since it's meant to be equivalent to (car (cdr x)), so if you wanted a safe list operation you would have to check it like this: (I'll use CADADR because it makes the issue more apparent)

  (and (car x)
       (cadr x)
       (cadar x)
       (cadadr x))

You would have to write this every time you want to see if there's a really CADADR, whereas if CAR and CDR can return NIL then you can just write (cadadr x) and CADADR can still be defined as (car (cdr (car (cdr x)))) and have the desired behaviour.