I have completely the opposite view. To me, all the "engagement" type arguments just feel like someone telling me that they still insist on using only rotary telephones, because it makes them feel more "engaged" with the telephone, "closer to the machine", etc.
So I don't find anything magical or special about having to manually manage the gears when a computer could do it more efficiently and relieve me of the need to worry about it. When I'm driving I want to be focused on the road and traffic around me, not micromanaging the way the engine is transmitting power.
Or maybe to go with a car analogy: what if we took away your accelerator pedal and replaced it with a crank attached to a fuel pump, so you had to constantly turn the crank to get fuel, and turn it faster or slower to manage the throttle and the amount of fuel going to the engine? You'd be much more deeply "connected" to your car that way, but would you rhapsodize about what a wonderful experience it was? Or would you see it for what it is: a task that can be done with more efficiency and less distraction by a different approach?