All the units I received had displays that were already totally dead, however you could see digits etc burnt in, even from the back side of the display i.e. through the silver backing. The one I'm looking at right now was burnt in clear enough that I can see that they had obviously spent significant time measuring a value of 011.8xx - 0.11.9xx on the 100V range in remote control mode... they should probably have turned off the display if no one was looking at it directly.
I suspect all my units came from the same source, maybe a production environment, though cosmetically they were pretty good - especially the first 2 - still had the sticky film on the display. The last one I got for the local equivalent of USD75 as it also has a main board problem. As I already had a spare display I figured it was worth taking a punt, even if I just keep it as spares for the other 2. Overall, I'm not impressed with the OLED durability (not just limited to this instrument, but OLEDs in general), but the readability is amazing. I personally wouldn't buy one new, but replacing the display is easy for someone with basic DIY skills so bargains can be had.
Regarding monochrome OLED displays, you can see that some are specc'd in the low 1000s of hours. In my own experience of other OLED devices, I've seen significant burn in after 6 months on always on devices with minimal screen saving functionality. I haven't noticed any screen saving at all on the 34450A so being totally burnt out in a year of always on use seems plausible.