Your proposed solution might work because it makes sure the high profits go the venue/artist, not the scalpers, but it only works if you can design such a system that can keep out/identify the scalpers. These technical hurdles is what caused the problem in the first place: if Ticketwhatever made a system with all security features working as intended, then there would be much less of a problem. The same technical hurdles would need to be taken for your proposed auction system. But the reason scalpers can make a living is because they can manipulate the market. By buying up all tickets, they create an artificial scarecity which enables them to ask what the mark will bear. Selling at a lower than facevalue price is just the cost of obtaining market dominance. Undercover agents with a licence to kill scalpers would be a good solution, but just realising that intervening in a free market is contrary to the US' capitalist ideals, would be an even better solution. Then the only problem is for the venues that don't get all the profits.
The proposed solution has nothing to do with identifying scalpers. Scalpers take advantage of market timing; they attempt to buy up as much of the ticket supply as quickly as possible and sell tickets at higher prices later. In a Dutch auction it's assumed everyone who wanted to buy a ticket has an opportunity to place a bid, and the price point is optimized based on all of the bids. Resellers wouldn't be able to win a majority of the tickets in the auction and resell them at higher prices (above what consumers were willing to bear), they could only sell to people who missed the auction or mis-judged their bids or have more disposable income later on.
The idea that resellers would sell at lower then face value price to obtain market dominance doesn't make any sense... there is an infinite supply of future events and the distribution costs for tickets is extremely low. Are you suggesting that Ticketmaster would be put out of business by resellers that originally bought the tickets from Ticketmaster? The "US capitalist ideals" you talk about are making the market efficient in the best way possible by optimizing profit, and if that means using a different market style like a Dutch auction then that more power to them. It is not intervening in any definition of the word.
Disclaimer: I'm not saying a Dutch auction is definitely the best answer, there are a lot of open questions there. I don't think your reply had any valid rebuttals though.