Maintaining the appropriate gear requires that you're focussed on the world around you.
Adding arbitrary other things requiring focus doesn’t seem like it would help prevent accidents.
A manual car sort of kicks you in the butt every now and then: “hey, you’re in the wrong gear. Stay sharp, and upshift!”
Other benefits, when I think about it, are that an automatic frees up one foot and one hand. I can drive with my cup of tea or coffee without having to shift, which is great. I don't know if it directly helps with awareness, but it helps me stay awake.