I have never had a driver open a door. Occasionally they don't even get out to open the boot/trunk if the customer has something to put in it and the customer does it all themselves.
The only time I have known a cab door to be locked is one News Year Eve when I was catching a cab home from the Casino and the driver urged myself and my friends to lock our doors as we drove through the city centre. He said that if we didn't the drunks would try to climb in, as no cabbie in their right mind services the inner city on New Years Eve. He said it was the one day of the year when drivers could be as fussy as they wanted to be about who they took for fares.