As far as I can tell, the problem with OLEDs at the moment isn't how thin you can make them, but how long they last; they seem to degrade pretty quickly.
Below 1mm I think this is all pretty masturbatory. You never hear anything about durability, tear/crease resistance or other packaging concerns.
It doesn't much matter (to me, anyway) if it's 0.0000001 mm thick if it has to be attached to another hard surface (window, wall) in order to not be damaged by simple handling.
I think the most important thing it is cost, and how cheap they are.
what if they were cheap enough to produce to be replacable.
If you can just stick on a display like a wall paper, in any surface, and if it was cheap, people wouldn't mind replacing them every 10,000 hrs. of usage. (If you watch 10 hrs a day, that's almost 3 years).
I wonder if OLEDs break down more or less independent of usage anyways like how a lithium ion battery can wear out faster from use, but is still wearing out even if you don't use it.
That's certainly the impression I've taken away from reading a bunch of articles on OLED displays. The failure rate is apparently still high enough (at decent yields) that they're not practical yet, and unlike back-lit LCD displays, individual pixels degrade at different rates, which is pretty bad for obvious reasons.