Not all drives had buttons. There were workstations (Sun Sparcs) which had. motorized eject mechanisms.

Used 10 of these workstations to copy my freshly downloaded Slackware Linux to the stack of 60 floppies it took. (Twice, so I wrote 120 disks, as at least one of the disks would have read errors on average). Each time one of the Sparcs was done, it did spit out the disk and I’d insert a new one, labeling the old one with what was written on screen.

Ah the hours I spent downloading and installing 100-200 Megabytes of operating systems.