I used zip disks quite a bit (as an architect) and never heard the click of death.
Before usb sticks, zip disk was the only way to move medium to large files, other than burn a cd.
The only true "click of death" involved physically damaged disks. It was possible for a damaged disk to also damage any drive it was inserted in. Outside of that, the "click of death" was really just the drive retracting and reinserting the head on a read error.
I used Zip disks extensively for audio and graphics work. Almost all the drives I encountered died after a while.
It was a design issue.
I experienced click of death using my zip disks at a school lab.
The disk breaks the drive, drive breaks the disk spiral made communal drives rapidly not an option. There was a utility available that I used to fix my disk, but then I only used my disks in my drive after that experience.
It was very common, or at least made out to be.
I never had it happen either, but I used SyQuest drives more, and then moved to CD-R (which was the real click of death for Zip disks)
I used my paper route money to add storage to my Mac 660AV.
My options were a SCSI hard disk, SyQuest or a Zip drive. I went with the latter. Since it was SCSI it wasn't appreciably slower than the internal HDD so I had a disk with MS Office installed, disk with all my games, etc that I'd swap out for what I was doing.
I was happy with my choice a year later when SyQuest had gone out of business and I had 4x as much storage as I would have had with just buying a hard disk.
Three years later I suffered the click of death and I was less happy. I used some hack I read on Usenet about cutting off the outer 1mm rim of the disk with nail scissors which let me rescue my data.