The Cape Horn sailor died for different, but related reasons. But once again, even when they are of the best design, and are used with caution, they are inherently dangerous. They register on our unconscious and conscious minds as a ladder, and ladders are relatively hard to get hurt on. But steps are a peculiar kind of ladder, a primitive style with a single upright in the middle and the rungs on either side, so there is little or nothing to contain the climber laterally. These details are very significant here, because of the rocking motion of a sailboat - the climber is always being pushed, in varying degrees, from side to side.
Rake is also an issue.
On a normal ladder, the climber is held onto the ladder, to some extent, by the fact that the ladder is angled to the building. Anyone who has climbed a fire-escape or similar vertical industrial ladder knows how much of a difference a little rake can make. On a boat, things are often even worse than ashore, since almost every mast is raked a bit aft, and most people go up on the aft face. On the other hand, mast rake isn't sufficient to be much help if you go up the front face. It is of paramount importance, therefore, that anyone climbing mast steps should be wearing a climbing harness, with a safety halyard of some sort attached to it.