I hate to say that a polynomial-time test isn't efficient because many people use that as the very definition of efficient, but my understanding is that AKS is incredibly impractical because the polynomial is ginormous, even though its asymptotic behavior is nice. So if you actually wanted to know if, say, a 1024-bit number was definitely prime, you wouldn't be able to run AKS on it in a "reasonable time" on a real computer.
Also, to further the discussion on probable vs provable: the probable tests are enough in our case because they tell us _provably_ if an integer is not a prime (that we care), but _probably_ if an integer is a prime (which we don't care here).
