I agree that we have a different understanding of how markets work. To hit what seem to me to be the key points:
(1) Markets do not just affect the long term structure of production relations (though they certainly do that). Prices of many goods and services fluctuate on a daily or even hourly basis. That is markets operating in close to "real time" to restructure economic activity in response to all kinds of changes in conditions.
(2) Markets do not just change when new entrants appear. There are other actions that market participants can take on shorter timescales to respond to changes in supply or demand. One key one is finding substitutes for goods or services that have become scarce due to some change in conditions.
(3) It's true that markets can't solve all problems, and that they work less well when there are non-market constraints operating, such as those imposed by a natural disaster. However, people who support markets (like me) are not claiming that markets can solve all problems; we are claiming only that, in cases where markets don't work well, other solutions (such as central planning) work even worse.
(One key reason for this is that most problems of resource allocation meet the conditions of your footnote #1: they are difficult to model and the input data is difficult to obtain. This applies to natural disasters as much as anything else: your apparent belief that such disasters are "straightforward" to handle does not seem to me to be borne out by what actually happens when central planners try to deal with such disasters. Btw, I think these problems are also computationally hard, in addition to the other characteristics you cite; that's another reason why markets, which are essentially distributed computation, work better than central planning, which is basically the Von Neumann architecture with a single-core CPU, with all its well-known bottlenecks.)
(4) If your criterion for working well is delivering results that are acceptable to an average person's morality, I don't think any system devised by humans has ever consistently done that in times of crisis. We're all still floundering, from that point of view. Markets are simply the "least worst" of the systems we've discovered so far.
Btw, I'd be interested to see your response to the "mixed" (market + non-market) method I proposed, in the post in this subthread that you originally responded to, for dealing with shortages in a crisis such as a natural disaster: some charitable organization (which could be the government, but does not have to be) buys necessities like food and water at the (increased) market price, and then distributes them to those who need them and can't afford them. This would allow the market to work, by giving an incentive to suppliers to increase supply (because prices are higher), but would also provide a mechanism for achieving a fairer outcome, by having the charitable organization act as a market proxy for the indigent. (Of course, it still leaves the charitable organization with the problem of how to fairly distribute its goods, but that problem is going to be there no matter how the goods are obtained.)