They get dimmer as they age and might also develop "burn-in".

This really isn't an issue these days if you research your screen. Rtings.com has a good series on their website and YouTube testing OLED burn-in, and there are many TVs where this is not an issue. Also check out Wulff Den on youtube and his videos testing the OLED Nintendo Switch. He does get some bad burn in after a year, but that's also because it's on a still image at max brightness and never turns off. I don't mean a year of standard usage. I mean 8,765 hours of it displaying the same image.

Screensavers became necessary again?

For OLED computer monitors: yep!

They were never necessary to begin with: automatically turning the screens off (or at least to 'black') is never worse.

Not just that. OLED TVs nowadays have a screensaver that kicks in when it detects stationary image for more than a few minutes.

They also shift the image around by a few pixels to prevent logos and tickers from permanently marking the screen.

And when turned off, they also try to level the brightness of individual pixels by displaying different patterns - again to combat "burn-in".