But it's not a password - it is not a challenge to a claim of authority in any fashion. Kirk doesn't prove he is Kirk by entering the correct code - after all, Chekov enters a string of symbols formerly used by Spock, and the computer neither recognizes him as Chekov (why would it, with the different string?) nor mistakes him for Spock (why would it, when he just previously declared "This is Pavel Chekov"?) as the result.
Authority to conduct the self-destruct is established separately. That is, it is when Kirk says "This is Captain James Kirk of the USS Enterprise" that the computer decides whether Kirk is who he says, and whether he has the authority to do what he is trying to do. Just as always in Trek, a voiceprint analysis seems to suffice (if there were more to it, Data couldn't so easily pretend to be Picard, say).
So the string of symbols is not a password. It is a "destruct sequence number", whatever that means. Might well be just a speed bump, a complex phrasing of the "are you certain?" question, to establish conviction the same way the mechanical doodads on the Nostromo did. Might be mode select, too, though.
Kirk can further select options such as countdown length. And Shane Johnson's interpretation that "Destruct Zero" selects the exact fashion of destruction (in this case, scuttling charges inside the saucer) is an attractive one, with options no doubt ranging from Destruct 0 to Destruct 47 if need be. Kirk entered the same symbol strings in both adventures, but we never learned that they would have had dissimilar results, so it's simple to argue that the strings affect the outcome somehow and that there would be other strings for other outcomes.
Timo Saloniemi