"The name paternoster ("Our Father", the first two words of the Lord's Prayer in Latin) was originally applied to the device because the elevator is in the form of a loop and is thus similar to rosary beads used as an aid in reciting prayers."
I would have thought the name was related to the users praying before entering to increase their chances of surviving the ordeal.
Although this mechanism looks scary it's actually fine.
The reason even its proponents accept you wouldn't build these now is that they have terrible accessibility, so they're only practical as an extra option.
We used to love riding in them at our university in the late 80s/90s. And when you proceed to ride over the top will the car flip upside down? We managed to scare at least one of our classmates into believe this could happen. The whole thing felt as exciting as a carnival ride in retrospect ...
despite that, it looks like the reason no new paternosters are built and existing ones are removed is safety. unfortunately this is considered to be more important than cultural heritage protection.
i have used one at the university of vienna. sadly it was removed almost 20 years ago.
For some reason I looked into this a couple of weeks ago, and discovered there's one in Amsterdam pretty close to where I often work, in the Grand Hotel Amrâth. It's supposedly open to the public every Sunday between 10am and 2pm. I think it's only the second time I've seen one in person, and the previous one has been demolished.
Only place I've ever come across one was Napier College, Edinburgh in the mid 1970s. I found it quite scary, and actually preferred to take the stairs. I seem to remember it was actually shut down, for undisclosed reasons.
I also used these ones in Edinburgh decades ago, and the same model at Leeds uni which was a similar vintage. The Napier one there is a story about a lecturer convincing two students it went upside down and if you tried to loop the loop you had to stand on your hands to do the transition... much hilarity when they appear upside down on the other side.
Neah, paternoster is quite a common elevator design in the west: https://en.wikipedia.org/wiki/Paternoster_lift