I used to be biased towards driving only manual transmissions, and I suppose I still am. My very first car had the tiptronic paddle shifting transmission, and as much as I regretted getting it over a true manual... It actually taught and introduced to me the idea of a sports car.
I attend track days often, and I see both transmission choices from participants out there... I've driven an auto transmission (not DCT), and it really makes the driving experience easier compared to shifting / downshifting in a manual, and it's just one less thing that you're doing while driving. I seemed to pay attention to corner workers better, and I was more comfortable in looking ahead while driving the auto... Because I was focused on only steering, braking, and the beloved gas pedal.
With that being said, wanting to drive with a true manual transmission is more about driving feel and experience more than anything else, I think. Yes, it's an additional tool to learn with at the same time. Most importantly, the reason why I choose it every opportunity thus far is because I want to feel the car better, and I want to feel the difference which I'm making to enrich my driving experience, especially at the track (heel & toe downshifting has been a wonderful feeling of art, once I learned it!)
Will I ever go for a car with an auto (DCT) transmission? YES... But only after I have a sports car with a true manual in my garage, first and foremost.