And what if I turn on the camera for a tenth of a second, take a picture, and turn it off. You won't notice the LED being on for a tenth of a second. Software makes it easier to prevent such things.

You definitely don't need software to add a little delay for turning off the LED, but sure, it would be slightly more complicated than just a dang wire.

Just wrote a test app on macOS that initializes the camera, gets the first video frame, and turns it off. You definitely notice the bright green LED being on for a split second.

You only notice it immediately if you're looking for it. I've gone minutes with the camera on before noticing the LED while I was distracted by other stuff on the screen.

Source code?

Why not both? It is trivial to make a circuit such that the LED is on if either there is power to the camera, or the software tells you to.

I would guess you could do the same with a circuit, even if that means you lose on flexibility (but given the concerns of many users, I'd say it's worthy).

A small piece of black tape or a physical shutter is likely a better choice. Who cares if the camera is on if it can't pick up anything?

The microphone, on the other hand, is kind of a bigger deal and still has that issue.