Explain your idea of this 10 BTC fee to the miner. Because Bitcoin is decentralized, you can't forceably withdraw Bitcoin from anybody. If you are suggesting a blacklist propagated by the miners themselves that would force withdraw Bitcoin from every transaction they would send then maybe that would prevent fraud.
The idea is as follows: to pay 1 BTC to V, you need to have an additional 10 BTC on a second address (like a deposit).
You then give V a normal transaction T1, and a second transaction T2. In case T1 is a double spend, V can use T2 to make 10 BTC go to the miner.
In the example you quoted, TX3Out needs to have at least 10.2 BTC in them (which are also owned by the person who wants to pay V).
Does that make the idea clear?
Your idea makes transactions 100% fraud free, however I don't see how that can be implemented for people who WANT to use the feature instead of everyone. Also, the main discussion point for Bitcoin right now is making Bitcoin very easy for the general population. Thats why you see those new Bitcoincards coming out. Your method also requires that everyone uses two wallets with every purchase. Making something like a Bitcoin card with that kind of anti-fraud system is impossible. Lastly, if V wanted to make T2 go to the miners, how would he force the said payment without having the private key to the wallet? You would need to have some sort of temporary escrow system in place always running ontop of the blockchain. Your ideology is admirable but not practical. Nice thinking though.