Why would you leave the computer running while not using it!?
Because I'm a professional and it's my main tool and I don't want to waste time. Although my system may "boot" in less than twenty seconds, I'd then need to: launch my favorite text editor + open all the files I was working on, launch my IDE (IntelliJ IDEA) + open all the files I was working on, launch the three browsers I'm using (in three different user accounts) + re-open all the tabs that were open, launch the VMs that are running, re-open the network connection to remote servers (SSH), etc.
I could script all that to re-open automatically but it would take quite a while to come all back up.
Not to mention automated backup happening at night and being SCP'ed automatically to remote servers.
I've got an 80+ gold certified alim or whatever the norm is and my PC at full-speed (100% usage on all cores) is dissipating so few energy that it has a passive cooler (no fan). It is so quiet while running that at first I'd sometimes turn it off thinking it was off, etc. At idle that thing is consuming next to nothing.
By the way: I own a very old Nokia 6110 or something like that (a dumbphone). That thing hardly consume any energy and can stay on for three weeks without needing to be plugged and is perfect for giving/receiving phone calls/text messages and is a fine alarm clock. Why do you even own a smartphone?
Regarding the tap water analogy: I think it actually makes a very strong case for leaving the PC idling with all its software / windows / tabs open instead of turning everything off ... When you turn it on you get water instantly. Not after two minutes. Not after twenty seconds.