During a midnight server room shutdown, that relay click was the ONLY sign we had. If it was silent, we'd have to reboot the whole system and hope for the best. Tactile feedback beats a blinking light every time, especially when you're tired.
Come on, it's just a server reboot. Not like you're defusing a bomb. Worst case you waste twenty minutes. People act like every late night task is some high stakes drama. A blinking light tells you the same thing if you just look at it.
Tyler_knight is right about tactile feedback saving you when you're exhausted. I always put my hand on the power supply to feel the fan stop as a second check. That physical signal cuts through the brain fog at 3 AM.