What is the origin of the hard drive light?

Well, I can say, as an engineer for MiniScribe (later Maxtor), it's exactly what it appears to be. It's an "activity" light. It was a way for us to tell that a command had been received through the interface and was underway. It was a debugging tool for those of us who, you know, built disk drives.

Floppy drives always had activity lights too, as you did not want to accidentally eject the disk while it was still being used.

It was also useful to see if your shell command was being executed as expected. Hard drives just continued to include what everybody was used to having on floppies.

There was a HDD activity light on the 20MB HDD for my Amiga A500.

Also, if you think about early mainframe computers, the only realtime feedback the operator got was all the activity blinkenlights.

Sometimes it's useful to know if the hard drive is active. For example, if the machine isn't responding in any way, but the hard drive is active, it may be that the system is overloaded and swapping physical memory to swap, but hasn't actually crashed. If this is the case, it may be best to wait for the slow operation to finish, rather than rebooting the machine.

These days, Windows is more stable and multi-task scheduling tends to work better, so there are probably fewer cases where it is useful.