As I understand it, plasma displays (which now seem defunct?) had issues with burn-in if presented with the same image for a long period of time during a single instance, while from personal experience AMOLED burn-in can occur even if the same image is displayed repeatedly over a long period of time. Screen savers would appear to mitigate the former, but not completely avoid the latter.
If the Windows taskbar is present 95% of the time that the computer is being used (with the other 5% being fullscreen applications), and a screensaver is active 40% of the time the screen is on, then the taskbar is still visible for 57% of the time the screen is on.
Maybe the tech has changed, but as of my first OLED phone 7 years ago, blue (the same color as the taskbar's Windows icon) was the fastest color to burn in.
Newer phones shift the navbar and status bar items a few pixels every minute. But the start menu icon is too big for that, so after a year or two, every time the user watched a movie in fullscreen, they would get a blue blob in the lower left corner.
You should just turn off the screen when you are away