How would you know that a double spend was in progress or not ?
I think a double spend has a potential window of 10 minutes ?
i.e. I buy an item say 20BTC, I walk out of the shop and I create another transaction signing the same outputs and send it.
This problem has been much discussed: if you only delay the sending of your second (conflicting) transaction by one second, it will have a very low chance of being distributed to the Bitcoin nodes. BDPIC could check if the transaction is known to a large part of the network (or just the main mining nodes) in order to minimize the chance of a loss.
The big risk factor for the BDPIC however comes from the Finney attack. Since it is difficult to pull off, it won't be a problem for transactions of low value though.
The main issue I see is that of trusting the BDPIC and the additional fee/hassle for the merchant. If the merchant uses some sort of payment service provider like bit-pay anyway, then this would be a non-issue. If he doesn't, then waiting/checking the network for possible double-spends could also be done by the merchant himself.
I remember somebody suggesting that such a listening-period could even be included as a feature in the standard client at some point.