I do drive a stick-shift car, and I've also driven (rental) automatic cars.
A stick-shift get you way much closer to the engine. A stick-shift driver can show it's emotions via the engine. stick-shift invites more aggressive driving. Your mental state "shows" thru your driving.
I learned on an automatic but quickly learned to drive my dad's car which had a a manual, and my first car, an air-cooled Beetle, was a stick. I also feel that driving a stick does make one an overall more aware driver. It's also why I'd never want a self-driving car.
Aware of what, though? And for what purpose? Being aware of the engine is not the same as being aware of your surroundings and hazard perception. In fact you can watch this in learners; at a junction which demands lots of traffic observation they make errors in moving off, or (more dangerously) fluff a gearchange while driving along and then look down or spend a few seconds panicking and recovering during which they might miss something happening in front of the car.
The programming language equivalent is clearly memory management. Yes, you can make it more efficient if you do your own allocation - but you have to get it right every time, and C offers you very little help to do this. C++ offers more, and Rust holds out the prospect of getting it right provided you can understand and fix all the compile-time errors. If memory allocation isn't critical to what you're doing this is a distraction that consumes time and effort to no result.
Not quite following the stick/automatic and human/computer comparisons. I also drive a stick - and I definitely think it makes me a better driver - but I also think that a computer could do a better job than me. The computer could be tracking many more things - environmental conditions, 360-degree obstacle detection, etc. - than I could ever do myself.
But what it doesn't do, yet, is know that you're going to take that hill home, so let's leave it in 3rd gear for the time being. Or that you intend to accelerate out of that next curve at the edge of traction, so let's not upshift as we ease up on the gas.
Desired power is really a one-dimensional intent, manual and traditional automatic transmissions are both leaky abstractions one of which forces a two-dimensional input, and the other of which gives a choice between a 2D input with different characteristics and a 1D input that isn't continuous but instead behaves very differently in different input ranges. CVTs are less leaky than either.
Wait, maybe I can understand not wanting to drive automatic, but fully self-driving cars let you actually do something entirely different with your time.
A stick-shift get you way much closer to the engine. A stick-shift driver can show it's emotions via the engine. stick-shift invites more aggressive driving. Your mental state "shows" thru your driving.