My history teacher brought this topic up in my class. He had a less violent theory about the reason for clockwise stairs, which is still related to the majority right-handed population.
That people carrying things up these staircases would be using their right hand to carry the item(s), and so would use their left hand to steady themselves on the wall (or the rope/rail/etc affixed to the wall).
He was specifically thinking of food/drink. Coming down would be empty, going up is full. He also said it'd be servants doing this, which is also why the stairs were always so small.
My experience is the same, from stairs to mountains, descending is much harder (maybe because we are tired of going up?). Anyway, I can see that intuitively, one can imagine that you need help to go up when you are carrying stuff.
If you're facing into the stairs, your toes are gripping the next step. Maybe the extra degree of freedom from your ankle makes it easier to get a steady foothold. Whereas if you're facing away, on narrow steps, your toe may be off the step. If you try to balance on level ground on the balls of your feet vs. on your heels, you can tell heels are harder.
If you're going up and you slip, your moving foot just slides onto the same step as your static foot. If you're going down and you slip, your feet are now separated by 2 steps instead of just 1.
All things that move across ground move best if they lean into the direction they're walking. If you're walking down stairs, leaning forward means leaning away from the stairs. Going up, you're just leaning into the stairs as if you're rock climbing. Also it's likely our bodies are just better at leaning forward safely than backwards.
I heard a quote somewhere that "If you go down facing it, it's a ladder. If you go down facing away, it's stairs." Some narrow stairs might be better treated as just strange ladders. 2 of the possible causes would be mitigated.
It is just way easier the way we are built, kids learn climbing stairs (and other things) way before they can safely walk stairs downwards. The smarter ones go backwards.
Standing on a step and stepping down is just ... complicated ... and requires considerably more body control.
The risk of toppling forwards and falling down the stairs (or the couch) is considerably higher than "stumbling the stairs upwards".
To add to the sibling comments, momentum is also a factor.
When you are going up, if you slip, your momentum will carry you into the slope. If you are going down and slip, your momentum will carry you into space. Then gravity will take over.
That people carrying things up these staircases would be using their right hand to carry the item(s), and so would use their left hand to steady themselves on the wall (or the rope/rail/etc affixed to the wall).