I was actually thinking that screensavers might make a comeback if OLEDs become the norm. CRTs could suffer from burn-in, even if the problem was minor enough that most screensavers were really for fun, and in the 1990s, screensavers were pretty common. LCDs don't see burn-in, so screensaver use seems to have kinda disappeared. Plasma displays can get burn-in, but never really hit very widespread use. But...OLEDs can.

Today, I think that most systems have some form of automatic power-down of the display if someone isn't using it, so maybe that competes with screensavers.