Currently 95% of people will be waiting 10 minutes, but it will open a door for the average Joe from the street to accept BTC as well, ultimately rewarding anyone who holds BTC currently.
I would love for people to start using Bitcoin on the high street, my life would be so much better in so many ways. But waiting even 10 seconds for a transaction (EFTPOS, VISA, etc....) is unacceptable. We either use 0 confirmations with at least the minimum fee and let the customer walk straight away or use a layer on top such as Bitpay. (If this takes off eventually VISA and MasterCard may support Bitcoin too)
The added benefit of a layer on top of Bitcoin is that we can pay in Bitcoin and the merchant can choose to have the transaction instantly converted into local fiat or remain as Bitcoin. (This will increase adoption)
If people are forced to wait 10 minutes for Bitcoin transactions ever (on the high street) this will forever destroy the reputation of Bitcoin in the minds of normal non Bitcoin people.
Also what makes you think that if we make Bitcoin clients relay double spends that it won't propagate as fast through the network (assuming the double spend is valid), there is no reason to suggest it wouldn't be as fast as the transactions themselves.
If the first transaction is 0 fee it might take some time to be included into blocks, the double spend with a fee then propagates faster before the first confirmation and eventually >50% of the network will see only 1 transaction. This might not happen all the time but it makes automated detection of double spends difficult. Your idea relies on the Bitcoin network always being able to detect the double spends correctly.
Also how do you move the coins without having the private key? This might be the most difficult part of your idea.