I can carry a full technical conversation while I heel-toe to rev-match the downshift into second at 60mph so the engine braking bleeds enough speed that as I throw it through the corner into town and lose a bit more momentum I hit the city street at exactly 30mph and can shift back up to third and tap the cruise control and coast to wherever I'm going. I'm not going to test it, but I'm pretty sure I could do it drunk and with one hand.
In my truck (automatic), when I'm climbing up to the Eisenhour tunnel, I want it to stay in 4th gear and I'll just give it more throttle, but it won't do that, it thinks it's smarter than me and downshifts to 3rd and I need to hear the engine scream all the way up the mountain. I always try to find the sweet spot for throttle input to keep it from down shifting which means that I'm running about 5mph slower than traffic, and that's annoying.
Since my only inputs are throttle and brake, I'm always trying to find the combination of those to put the transmission in the gear that I want it in rather than just sliding the stick and putting it in the right gear.
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.
The usual cause is hitting gas instead of brake, followed by disorientation (expected = braking, result = acceleration, usually strong acceleration). Humans, especially elderly, can't reorient quickly enough. With a manual, you're depressing the clutch as well, so the mismatch is much lesser.
This is one of the best arguments for stick shifts: even if the extra layer of control may take extra effort, the thought process of having to shift, feather the clutch, think about what gear you should be in, rev match, engine break, etc makes you a better driver