It's almost certainly because staircases were 1) hazardous as hell, 2) going down is way more dangerous than going up, 3) clockwise puts the dominant hand/foot

It's almost certainly because staircases were 1) hazardous as hell, 2) going down is way more dangerous than going up, 3) clockwise puts the dominant hand/foot on the side with the biggest width when descending. There was an article here on HN a while ago talking about how the stupidly designed staircases were responsible for the Victorian trope of "falling down a staircase to your death."--the ones for servants were especially poorly designed.