What if someone created a Bitcoin Exchange where in order to trade, you first place the order on the site. Let's say it's a sell order. Then the site gives you a Bitcoin address to send the funds to for the order. You send the BTC to the address, and when the order is filled the fiat currency is sent to Dwolla. It isn't imperative that the payment processor be Dwolla obviously, I just can't think of a better payment processor for this use-case ATM.
It might not be good for some uses because of the increased transaction fees compared to MtGox (bots and trading methods that use many transactions), but there would be less trust involved, as the site would not need to hold funds for long. One would only have to trust the exchange to not run away with one's order funds while the order is still in the book.
What are the reasons this would not work?
An exchange that would use
Trustless, instant, off-the-chain Bitcoin payments, would have similar idea behind it, but the transaction to place the order would be instant, free and off the blockchain so it won't bloat it.
Bitcoin system assumes that a business with a good reputation has the integrity to deliver goods in exchange for received bitcoins and would not disappear with customers money because it had to spend a lot of time to build the reputation in the first place.
The bitcoin system makes no such assumptions. Bitcoin is just a tool. What you do with it, whom you choose to trust is up to you.
Saying that bitcoin security is flawed because people choose to give up control of their private keys is like saying that the security of a door lock is flawed because you gave the key to a caretaker who emptied your house while you were on holiday.
Of course, for the economy to function, a good trust management system is required as a layer on top of bitcoin. But the two systems are independent of each other.
Bitcoin as piece of code is a tool, and everyone free to use it as they wish. Bitcoin as payment system encourages businesses, that have to hold customers bitcoins, to steal it and bankrupt the company. The assumption was that Bitcoin as payment system would work fine for exchanges and eWallets because customers would be able to make informed decision about the company based on its reputation.
