I can confirm this - had for 11 years manual shifting bmw (3 series e46), some 2 years ago it sorta died and we bought automatic (5 series f11). The amount of cognitive load is much much lower (also thanx to laser projection of speed and other info on windshield, this is by far the best security car feature in last couple of decades) to the point it becomes boring way too easily.
Once or twice I got into situation where I was very tired and was almost getting sleepy, this would never happened with manual shifting and the need to be more engaged with vehicle. Also, for 98% of the situations, 1 hand on steering wheel is enough so you can handle stick, and the rest of situations you should be able to anticipate if you are a seasoned sane driver.
Another data point - once I had to take my wife's car for 1500km drive to take it back home. It was old Toyota without any cruise control, not ideal for such long drives on European highways full of speed radars. It was the only time in my life when I could drive this run through whole night alone with basically only stopping to refill, buy vignettes or go to toilet (5pm-8am drive). Normally on this road, I get too sleepy around 3-4am and my eyes literally start to close even if mind still can go further, and I have to sleep a bit. Was way too pumped from all sensory input. But I am sure I don't want to repeat this.