It is a proven deterministic test of primality. We already had those before AKS, and they are significantly faster than AKS (even the various improvements). B

It is a proven deterministic test of primality. We already had those before AKS, and they are significantly faster than AKS (even the various improvements). But they don't check all the boxes that are useful for stating things in computational complexity proofs without a paragraph of weasel words. So from the theory side of things, it's great since we don't particularly care about the actual execution time, but the asymptotic behavior and whether it is solidly shown to be in P. Lots of math packages have deterministic primality tests, but none use AKS as a primary method, because AKS offers no benefits over other methods and is many orders of magnitude slower. For inputs of special form, there are various fast tests. E.g. Mersenne numbers, Proth numbers, etc. The fastest method depends on the input size and how much work you want to put in. For tiny inputs, say less than 1M, trial division is typically fastest. For 32-bit inputs, a hashed single Miller-Rabin test is fastest. For 64-bit inputs, BPSW is fastest (debatable vs. hashed 2/3 test). The BLS methods from 1975 are significantly faster than AKS up to at least 80 digits, but ECPP and APR-CL easily beat those. ECPP is the method of choice for 10k+ digit numbers, with current records a little larger than 30k digits.