Here's my guess. Falling down a staircase is way worse than falling up it. If it's clockwise, then if you hug the outer wall (with the less steep steps) as you go down then your dominant hand can hold the wall (and any handrail).
From my years playing Minecraft, it's probably got a lot more to do with the layout of the upper room. Like you don't want your spiral ending toward a wall, you want it ending toward the room itself.
It might just be because architects / builders copied each other. There are loads of little infrastructure details that vary from country to country with very little reason for the difference other than "that's how they are here". For example the gaps in American toilet stalls, or even the shapes of the toilet bowls - way shallower in the US than the UK. Why? Just tradition I expect.
Unless walking backwards, it is normally more common to trip and fall over forwards; when walking upstairs, you could just fall on your hands, since there's stairs in front of you. It is very difficult to trip and fall over backwards, specially when walking upstairs.
Falling upwards generally comes with less potential for injury. Falling backwards when going up is probably about equally bad regardless of clockwiseness.
Here's my guess. Falling down a staircase is way worse than falling up it. If it's clockwise, then if you hug the outer wall (with the less steep steps) as you go down then your dominant hand can hold the wall (and any handrail).