Caps lock because it doesn't do anything like enter or other keys might do and if I see the light blink then I know that the computer/keyboard is not frozen.
Interestingly, I use the shift key for the same reason of "it does nothing". Who knows if I left half a command in the terminal or something like that.
I don't have a caps lock led, but that's a good idea!
I've never heard of a frozen keyboard. That is definitely not an issue to worry about every single time anyway.
Plus when it works you need a second press to turn it back off before entering the password. Way too much work.
I usually use the up key as that is one of the few buttons I know of that will open the password field (I'm assuming down also works, but I haven't tried many others). I usually turn my monitor off (can't just leave it on as it's in my room and if a cat moves their ear too quickly that will wake up the screen and I can't have that while I'm comfortable in bed) at night, so the first time I use it in a day I will turn it on, smack the up arrow and the login screen is gone before the screen turns on all the way. Which is a little sad I don't get to see it much since I did pick out a theme and background for it, but can't be helped.
Wireless keyboards go to sleep and can disconnect. Modern ones are sometimes smart/quick enough to send the first keypress but older ones less so. Also if the computer's off spamming caps lock won't turn on the light and let you know to hit the power button.