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.
Sometimes necessary for tricky hill starts, I won't fully remove the brake until I feel the accelerator moving the car forward, but that should fit within the GP's 'little bit'. EVs should be easier on hill starts because there's potential for less latency between input and power delivery, but I dunno; I don't care for driving east across downtown Seattle regardless of if I'm in an all gas or a PHEV.
Hell, my 1987 Toyota pickup had one. You could put it in 1st gear, let the clutch out and then turn the key to start, if you were on a very steep hill. Comes in handy offroad.
My 2014 PHEV does have a button, but I don't use it, because when I'm in the situation that needs it, there's usually cars behind me, and that's not a good time to test and see how it works.
I also imagine that two-foot drivers would prefer for the effect of pressing the brake to be smooth, and having the slightest touch instantly reduce motor torque to zero could be jarring.
I've done it a few times to make people following too closely back off of my rear bumper.