There's some corner cases where using both can be beneficial (like heel-toe downshifts with manual gearboxes, or changing the way torque is steered on AWD), but they're generally pretty far removed from the way that driving is usually taught or performed.
But starting on a hill in a conventional automatic with a torque converter also involves either rolling back a bit or pressing the accelerator a bit before releasing the brake.
Felt deeply in San Francisco. I think newer cars rollback less than older cars. Either way, it is unnerving when driving in Lombard street.
You can't pay me enough to drive in SFO in a stick shift.