OLEDs will always be subject to burn in due to how they work. Since each subpixel is for a SINGLE color, they will age differently because they're not all going to be on at the same time (ex: a pure red will not have green or blue subpixels active, so red would age faster than the other two if left on for days). The larger ones, usually blue, will need more voltage to excite it than the smaller ones (almost always green, as we see more of the green spectrum than blue--look at a CIE colorspace chart and you'll see very little "blue" compared to green). More voltage = faster aging.
This will NEVER be eliminated, and will always happen using current OLED technology (read: need alternative to currently used organic materials not subject to electric decay/aging).
HOWEVER, don't worry about this. For a user to actually introduce image burn in you will need to have your screen BRIGHT (250+ nits at least) AND have a STATIC IMAGE being shown for DAYS.
I'm 99% positive that any image burn in reports, that have NOT done the above, is not image burn in but Image Retention (aka image persistence).
Image Retention is TEMPORARY, and is mostly from electrical build up in display components and will go away once the build up has discharged (pixel is off for a while). On LG OLED HDTVs there is an option to "clear panel noise" which is what this does; don't know if other manufactures have a similar option available.
Alternatively you can add build up to improve screen uniformity by looking at a pure white screen for a few minutes. (google "jscreenfix" to see what I mean by colored noise. There is an old jscreenfix.jar file that's no longer hosted on their site for offline and full screen use. I don't know if it would work on androids as it was made back in Windows XP days).
Again, I'd like to put emphasis on the difference between "image burn in" and "image retention". At a glance they will look identical.
How Samsung has their "always on display" may make finding which you may have difficult. It's possible that the screen is still getting power even with the phone OFF depending on how the circuits and internal components draw power from the internal battery (read: OFF may be an extreme form of SLEEP where the absolute minimum of power is flowing through components if they used some more exotic designs for the sake of reliability).