No matter how good the automatic transmission is, it just can't anticipate.
Am I slowing down because there's a slow car in front of me temporarily, or will I actually come to a stop because of a red light?
I can see there's a sharp corner coming up, so I would have shifted down before it. That would both slow me down and give me torque to accelerate around the corner. The transmission can't see. So I will have to brake quite solidly to burn off my speed, wasting energy.
And so on. I used to love those twisty mountain roads when I had my SAAB and 5 gears. Now my automatic Merc isn't anywhere near as much fun.
"Yes, I drive stick shift."
"Nope, all automatic."
Etc...
FWIW, I do drive stick, however current cars are automatic.
I feel driving manual encourages a deeper focus on the road ahead and deeper connection with how your vehicle operates. You tend to plan ahead a bit more, be more aware of hills and curves, cars slowing down ahead, etc. – anything that'll make you need to switch gears. You could still have distracted driving, especially on highways, but driving stick lessens it, I think, though I have zero evidence to support that feeling.
That brief moment in an automatic where the car figures out you wanted a change kills the experience of the machine being an extension of me.
Is this a US specific question? In Germany 92% of cars sold are stick shift so driving automatic (usually means paying extra for the feature) would be the exception.