> In real life, a human doesn't do classification tasks with the System One part of their brain, they use System Two.

Huh? I guess that depends on the exact definition of "classification", but I think the bulk of basic classification tasks we make every day to make sense of our surroundings, such as object recognition is definitely done using system 1. So is higher-level "stereotyping" or anything you could described with "I know it when I see it".

Because those responses can be incorrect or even harmful, you would sometimes make use of system 2 to correct them - but that doesn't change that the initial response is from system 1.