Maybe people don't actually believe in merit, in near mode. Maybe they think they do, but they are really thinking about status.

Distributions based on merit (that we don't recognize instinctively) simply seem unfair. Distributions based on tranparent luck seem like everyone at least had a fair chance.

Maybe the real problem with money is that it usually belongs to people we personally don't know, so we don't know what exactly they did and why exactly should we respect them, so it feels like they really don't deserve the money. And the rest is rationalization.

I would assume that people who run the barbecue are (1) Aware of the problem; (2) Have incentives to deal with it; and (3) Are not entirely stupid. Given this I am not sure why do you think that what they are doing now is not "the right answer".

I think that (3) is not a good assumption to make, and I wouldn't word it that way. I know lots of artists who have never heard of sealed second-bid auctions (also known as Vickrey auctions), despite those auctions being the optimal way to sell artwork or commission slots online. Are they entirely stupid? No; they just have limited knowledge. Similarly, the barbecue auction problem has a potentially nontrivial complication: there are 5 different varieties of meat sold by the pound (and each variety of meat can either go into by-the-pound orders or sandwich or plate orders), and many people would like either their entire order, or none of their order. How do you find the optimal set of orders to fulfill, and what price do you charge people for those orders, in a way that doesn't skew their bidding incentives?

It's a solvable problem, of course, but it's the sort of problem you'd want to hand off to an optimization guy to solve for you, especially if your core competency is barbecuing meat.

For example, raising prices might be good in the short term but turn out to be a very bad idea in the medium term.

It might- it's possible that once people could get it by paying more money, instead of more time, it would lose some of the specialness and people would go there less. But it's not clear to me that they would ever reach the point where they don't sell out of meat, and maybe they have to be open for dinner too instead of just lunch.

But it could also be that the steady-state long-term price of their brisket is $40 a pound, and they've been selling it at $17, and that it is a fantastic thing over the medium term.

(Also, I feel I should mention, since it may not have been obvious: they do allow pre-orders, if you're willing to pre-order by about a month. The amount of pre-orders they allow is obviously capped, so that there's still BBQ available day-of. Auctioning off meat should start as a small percentage of their total quantity moved as a test, and then expanded or contracted as desired. So long as some of it is available by waiting, it is unlikely to lose the popularity.)

What is that problem and, again, what does it have to do with temporary shortages of high-status goods?

Basically, not enough people thinking like economists.