Indeed.
It's hard to press when I'm not there, though. Especially if I did press it before I left. Hell, I can't even tell if the monitor is on or off, even logging into that machine remotely. Modern tech, eh? And even when I am on remotely, my screen doesn't move... the video output stays on the lockscreen while it sends the images to me.
I think my tech turned it on to do a staff induction and then forgot to turn the monitor off (why would he turn my monitor off? He's probably never needed to do it).
But, unfortunately, being a school screensavers are pretty pointless (how would you like your lesson to be ruined every ten minutes while you'd left the work up on the board for the kids?), and being a computer in the IT office it's not subject to the 10pm shutdown that all other machines are (because if that goes wrong, God help you... even though the servers can be accessed, you're going to want a machine that's been kept joined to the network with a local copy of your profile if something goes wrong, I guarantee you).
And, literally, in 25 years of doing this I've NEVER SEEN BURN-IN. I think the monitor has just hit that age - it's at least 6-8 years old, I think. The logo that's now burnt-in a little has been the same logo in the same exact position for the last 4 years. I know, because I put it there. It honestly hasn't appeared on even the dozens of same-age monitors we've had to bin due to age (P.S. As IT, you should use the worst stuff you have, so you know that your users are just whining when they complain about your equipment). We got a lot of ex-Olympic stock at one point and I'm still churning through it until it dies rather than spend money needlessly. Casualties of burn-in? One monitor, that's been used more than ANY OTHER in the entire place.
So, to be honest, it's not my fault, and still not a concern. Hell, I might actually go for widescreen with the next one...