According to Wikipedia they've always had them. Doesn't having someone like this on the train mean it's not really "driverless"?
I don't know how they'd do it on the tube. Presumably door closing would still require manual control.
The door closing works well for the DLR -- the PSA checks all the doors are clear and then shuts them all at once. This probably isn't viable for a tube because platforms are smaller and more congested.
What for? The doors can be on a timer (station-specific if necessary)