The electron guns in CRTs also take about 30 minutes to warm up. Before then the black level is pretty high and the image is washed out. So there is benefit to running a screensaver on a CRT but OLEDs do best when just put to sleep quickly.
When was the last time you looked at one? Was it todsy? I own half a dozen PVMs and two PC monitors and have been looking at CRTs consistently since the 90s.
It takes about 5 second for my LCD monitor to wake-up after a sleep, which is a bit annoying. A screen saver disappears in a fraction of a second even on old hardware.
