Airline booking numbers used to just be the sector number of your booking record on the mainframes HDD.

That’s why they were constantly recycled?

This is such a simple scheme.

I wonder how they dealt with common storage issues like backups and disks having bad sectors.

They're likely record based formatting rather than file based. At the high level the code is just asking for a record number from a data set. The data set is managed including redundancy/ECC by the hardware of that storage device.

My jaw just hit the floor. What a fascinating fact!

source?