This ignores the fact that even if you explain quicksort to a random person and give them a list of a few thousand numbers they can only look at one at a time y

This ignores the fact that even if you explain quicksort to a random person and give them a list of a few thousand numbers they can only look at one at a time you will invariably find out that most of the people will get it wrong most of the time. Just because you think you can imagine the execution of an algorithm given its description doesn't mean any random human brain can; doesn't mean even you can, if pressed, executed a really complicated program without errors. The error rates we get on modern computers are scary for most "algorithmic" problems.