So... my first reaction to your comment was "why don't they just turn this into an actual auction, with no price limits? This seems like such a good solution that I feel like I must be missing something."
However, thinking about it more, I think there's a problem with that that's hidden by the nature of the United debacle.
In that situation, the passengers had tickets, and they company was trying to seat their own staff. That is, the potential buyer was the airline, and the sellers were the passengers. So in that scenario, auctioning makes sense, because you can literally flip the buyer and seller roles.
However, in a typical overbooking situation, there are more passengers than seats, so it's unclear who the buyer and sellers are, because none of the "sellers" actually "own" anything definitive. If the tickets are all infinitely valuable to each passenger, no one can get on the plane, and there's a sort of stalemate. Then I suppose there would be a cost to each passenger, and an incentive to accept a price, and it wouldn't be infinite anymore. But in general, the cost dynamics seem weird to me. But then again, I'm not an expert in this.
At some level, overbooking seems indistinguishable from fraud--which can also be profitable for its practitioners.