Shifting is just part of driving. It means you have to pay attention to speed, Rpm, and braking points. It just makes driving more engaging, which reduces distraction. It doesnt make driving easier. If anything it makes it harder. But the benefit is that it reduces complacency.
When i am driving. I am driving. Im not doing makeup, eating, messing with the radio, texting etc. Part of that is driving stick. It keeps you engaged in driving. Thats not to say its impossible to be a distracted driver in a manual, just that its easier to get distracted in an auto.