Thinking about them, can't they be made safish with a dectors for stuck limbs ? (Basically a big button the width of the elevator on top of the elevtor and on top of the ceiling.)
I don't know if it is typical or not, but at least some of them have that. I saw one in Prague, Czech Republic (there was an ACM contest hosted on Czech Technical University).
When you look at the frame, where you enter the elevator ("door", "door frame" or however it should be called):
- a part of the floor is on hinges, so if you had your foot stuck between an oncoming floor board and cabin floor while traveling up, it would "open" and trip the safety,
- upper part is actually a freely hanging piece of wood, so if you had your head or limbs sticking out while traveling up, you would lift the piece of wood and trip the safety.
No idea about the actual cabins -- for example if you kept hanging on the floor while the cabin travels down onto you -- but I suspect that the top of the cabin works similarly to the top of the "door frame". If my memory is correct, the cabins also had hinges near the edge of their floorboards (e.g., foot between the floor and the cabin traveling down), but no idea if these also stop the entire system.
Only the visible chain mechanism when overriding top or bottom looked unsafe to me, because I stick my hands everywhere :)
PS: These safety parts looked almost as old as the elevator, so if they weren't a part of the original design, I would guess they were added a long time ago...
EDIT: I actually found a mention of regulation from 1982 stating that the sliding upper parts are mandatory both on the cabin and on the "door frame" and moving them must stop the elevator. The hinged floorboards on cabins and floors are also mandatory, but there is no mention that they should also stop the elevator.
See [1] (in Czech) for pictures.
The one at the university of Leicester has trip lines that will trigger an emergency stop near the top of each "door". A foot or rom would certainly trigger that.