Sure. But consider airlines, and the revenue management they do, as a contrast.

The basic problem is that there is no single price-per-seat at which it is profitable to fly a plane. Imagine the demand curve as something like $1000/x, where x is the number of tickets sold on the plane. Regardless of the price you pick, your total revenue is going to be $1000, and if the plane costs $2000 to fly, you can't pick a single price for every ticket such that the plane is profitable to fly.

But suppose you could offer different customers different prices. The person willing to pay $1000 is charged $1000; the person willing to pay $500 is charged $500, the person willing to pay $333 is charged $333, and the person willing to pay $250 is charged $250. Now you've got a plane in the air, and $83 in profit (and another person paying $200 would get you up to $283 in profit). But this required you knowing which customer was willing to pay what, which is generally done by time-segregation (the amount of time you book the flight in advance, combined with the number of seats left on the plane) which is itself determined by sophisticated modeling.

There doesn't seem to be a public outcry about revenue management for airline tickets. Perhaps this is just because people don't understand what's going on underneath, or adjusting prices with time feels appropriate in a way that adjusting prices with supply doesn't, or because it's been this way for ~30 years and people are used to it now.

If you price the barbecue high enough that exactly the number of rich customers arrive that will buy all the barbecue, in a week from now those customers will be tired of barbecue and there won't be other customers to replace them.

This is not a problem for auctions, because the price drops when the demand drops, so long as the minimum price is set so that the market always clears.