I learned to drive stick at 34 just for fun. Now own a Mazda 3 and MX-5. Worth it. It's not about out performing an automatic transmission it's about engagement. For some people that's not going to have any value. For others there is no going back to numb econoboxes with automatic transmissions. It's a shame more people don't get over the hump and get to see what driving can be vs. what it is for most.
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?