My wife is a pro with a manual, and even has efficient driving practices, but she still prefers the auto because it's easier for her to eat breakfast in the car on her way to work.
I used to eat, shave, and brush my teeth while rowing the gears in stop and go traffic, opening the door to dump the whiskers and spit. Of course, I am a pro at knee driving
I can hold a more steady line around a corner with knee driving than the typical motorist.
I'm not advocating these things, just sharing my previous experience. I also see no reason why texting should cause more accidents, but obviously it does. Holding the phone out in front and taking quick glances is similar in the amount of time it takes to check mirrors, so I would think it would have a similar amount of risk. It seems people spend more than a quick glance looking at their phones, and do so while in close traffic.