But you can pick those other values as basis vectors, and they are just as good a choice as alive/dead. The only reason that you can say "the cat's brain doesn't experience those other states" is that you've presupposed a classical cat, that has some preferred basis. But this is just begging the question. We only get classical behavior when the wavefunction gets entangled with a classical object, but the math predicts you should also have non-classical "half-here" objects that would experience non-classical "half states" - and those are actually infinitely many.

So how did the classical world arise? Or how come we happen to be in the classical world, when there are infinitely many other non-classical observers? And note that the anthropic principle doesn't help here - all of the real laws of physics are the same for those other observers, you get the same chemistry etc, it's just the classical approximations that fail.