The only problem that I see here is if we are dealing with people in different countries. The bank transfer will take few days and in the mean time the exchange rate might have changed drastically. In other words there is the possibility that one of the parties is willing to walk out of the deal, creating massive problems.
What I am looking for is an exchange where I can trade with a high level of anonymity. The regulatory environment in many countries is changing with countries banning trading and/or mining of cryptocurrencies.
The weak spot in mining and trading is the conversion from crypto to fiat, so I am trying to find a good way to do this in the safest way.
By the way, I naively thought that localbitcoins was decentralised since the transaction is happening peer to peer.