> The rest of the "Extended BIOS Parameter Block" looks like it isn't relevant data, like the volume label or the volume's serial number

No, that's the exact reason why OS/2 checks the OEM ID. The volume label was initially used to detect disk swaps (so that if an application has open files on disk 1, it does not destroy data on disk 2 by writes after the user replaces the floppy in the drive, which could not be detected in hardware until much later, and even then not unless you were using a Mac, basically).

Of course, the volume label is user-set (so duplicates are possible), and more often not set than meaningful in any case. So, DOS 3.3 added the (unique-at-format-time) volume serial number. Which was always all-zeroes (or garbage) on pre-3.3 disks, hence the need for the OEM ID check.