The auction you mentioned would not be a good one. If bidders don't know that they will be protected by a single clearing price, they will drastically reduce their bids. It would basically guarantee that everyone who won the auction would be immediately under water. This risk aversion leads to people bidding under their expected value of the stock, and instead results in them choosing a price that they're much more (e.g. 90%) confident will be good.
Generally speaking, the highest single price that clears the entire demand is best, and would result in bidders submitting their most honest and aggressive bids.
The problem with IPO "auctions" is not that they're at one price, but that they aren't really auctions at all. It's just a private negotiation wrought with many conflicts of interest. Dropbox, for example, had 25x more demand to pay $21 a share than actually traded. And instead of raising the price further to clear the market at a fair valuation, banks instead used this archaic matching system to give shares at below-market valuation to themselves and their friends in hedge funds.