OLED displays are gorgeous, but are still not ready for prime time, even today. The Pixel 2 phone OLEDs (the high end model) are showing burn-in effects after a week of use. And those displays have a decade of manufacturing and process improvements over the 1273A displays.
Tell that to LG: their OLED TVs are holding up just fine, as are many other OLED products. It comes down to the specific display quality, not the technology as a whole.
My friend that bought an LG OLED TV did tell it to LG... burnin and color/brightness shifts showing after a few months. Modern OLEDs are a LOT better than earlier ones but they still seem to have issues. The blue LEDs seem to be particularly troublesome. The TV was fantastic looking when it was new. I look forward to the day when OLED screens can be trusted to last more than a few thousand hours.
An early one or a recent one? I thought that reviews of recent ones (like, the past year or two) indicated very good resistance to burn-in, supposedly comparable to CRTs.
FWIW, my home cinema is built around a Panasonic plasma TV, the other "ermagherd burn-in!" technology, and it's almost 9 years old without a hint of burn-in. I watch enough vintage 4:3 pillarboxed TV that one could imagine the center area being worn out more, but I can't see any such damage, even when showing a blank white screen, and knowing where to look! So if there is any wear, it's below my visual acuity, and I'm really, really, really good at color.
Of course, my plasma is used as a TV, and the Apple TV settop box has a screen saver set, so it's living a normal life. Plasmas used as info displays in airports, digital billboards, etc. absolutely do experience burn-in, just like CRTs used for that. (And even some LCDs.)
Note that plasma experiences another effect, transient image persistence, which is sometimes mistakenly called burn-in. But it's actually a charge build up in the pixels, and it manifests as the opposite of burn-in, in that those pixels get stuck slightly
brighter than they should be, whereas burned pixels lose brightness. But this goes away after a few minutes, or by just playing some video to exercise the panel.