Kolmogorov complexity is only unambiguously defined asymptotically, and "asymptotics is merely a heuristic". It is also uncomputable. So, to use entropy arguments for passwords, the only correct way I could think of is to generate long and (elementwise) random passwords.
You asserted that Kolmogorov complexity will disagree with Shannon entropy in this example, so how do you know what the Kolmogorov complexity of this example is?
It is a random variable in this setting, as it is a function of the randomly generated password. Given a deterministic sequence, you find the definition of its Kolmogorov complexity in textbooks/Wikipedia/etc. By saying the Kolmogorov complexity will disagree with Shannon entropy, I meant the former, which is a random variable here, does not converge to the latter, contrary to the standard asymptotic setting which probably gives people the idea of using entropy to characterize password (I don't know, don't work in security).
The point of my original post is that the asymptotics break down here, and this phenomenon is not poorly understood, at least in some other communities. It is not meant to provide an alternative that is always well-defined and useful, although as I said in the grandparent comment, there is the useful implication that you can stay safe by sticking to the asymptotic regime.
It's easy to calculate an upper bound on the Kolmogorov complexity of a given value (you just have to exhibit a Turing machine that computes it), but very hard to prove a lower bound (you would have to prove something about all possible Turing machines).
