NFC will work when your battery is flat. NFC (Near Field Communication) doesn't actually use radio waves, it uses magnetic coupling like a transformer (therefore it neads to be Near). Hence the power for the SIM card (which will double-up as your banking and Oyster card) and associated NFC circuitry can come from the reader.
NFC can work both ways, so if the application on your phone would like to, the telephone can become the reader and communicate with a card (in this case your telephone battery would need to be working). Hence telephones can also communicate with each other using NFC. NFC can be thought of as being the same standard as is uses for contactless cards and passports but the device can be both a reader or a card. The interesting thing about NFC is that the "pairing time" between reader and device is very fast and communication can start virtually instantly a device comes into the magnetic field. This is not the case with Bluetooth.
The extra hardware needed in a telephone is very small, an antenna and an NFC IC. With NFC you will no longer need to carry your wallet, the idea is all your cards will be in the SIM card in your telephone.
The reason it is not taking off has nothing to do with the technology but the business case. Who is going to control, define the security and pay for the SIM card? The banks? The telephone operators? London Underground? The telephone operators will want a cut from every transaction made on the card, why should the banks give them this money? It may be more convenient for the customer and interesting for the telephone operators but why should the banks push a solution that will lose them money?
This is a common problem with new ideas. If the person who pays is not the person who benefits it is time to ring the alarm bell.