It's already done. The docklands light railway in London is more complicated than the metro systems of most cities and it's been driverless since the 1980's
http://en.wikipedia.org/wiki/Docklands_Light_Railway#Map.
On the other hand, it still has a staff member, 'Passsenger Service Agent', on every train to deal with customer service. They are also trained to drive the train at very low speed (I'm guessing <10mph) when the automation fails, which it does occasionally.