When I used to drive auto I could literally have my phone in my right hand with my left hand on the wheel at all times if I wanted to...
The hard part of texting while driving stick is taking your eyes off the road, not having three things to manipulate with only two hands. That's like saying it's impossible for humans to drive stick because there are three pedals but only two feet.
What's your driving style like? I imagine the people who accelerate as quickly as their car is capable of, consistently drive 15-20 over the speed limit, often have to speed up and slow down and dodge between lanes will have to shift a lot more than the rest of us.
It just strikes me as weird that other people think it's impossible to drive stick and text at the same time. Sure you can't do it safely, but that's nothing to do with the transmission.
I learned stick on a working holiday, driving utes in Western Australia
He probably just drives something made in the last ~15yr. In a modern vehicle the power band is wide enough that you have about 3 gears that can be used in any given situation and the gear shift is basically a 6-way toggle switch. You could definitely use your phone if you wanted to.
I used to eat a bagel on my way to work in stop and go traffic with my gear shift hand and that's in a 25yo vehicle with a really long shifter and such little power you really only have one good gear for a given situation. In a vehicle like that it is much harder to be distracted and drive comfortably.