There are actually plenty of oled displays in out or in development right now that could work, though would be larger in size. The problem is that oled is moving quite rapidly from generation to generation. Each generation the "old stuff" is basically scrapped and they move on to new production lines. Unfortunately with new capabilities, technologies and new interfaces the lines physically cannot make the old stuff any more. In LCD the underlying technology is pretty much done, changes are evolutionary rather than revolutionary with updates in backlighting and edgelighting being the current forefront, so one line can run new product and switch back to old at will.
The main focus in oled development is for things like cellphones, which have a very different design focus than what a dive computer manufacturer needs. Stability and long term availability of product has not been a focus, 18 months max start to no more product available anywhere. Not to mention that the technology changes would require a dive computer to use a more traditional video system vs dot matrix which means more development upfront. That may or may not be a positive depending on your point of view though, as it would make your dive computer look more like how your smartphone looks.
That being said it is still the best technology out there. Self lit screens provide the highest contrast ratios and are seen best under water. I have been proud to wear my uemis in the past and will continue to be proud to wear it even as I wish for a quality company to purchase and support it.
Hopefully as we have now moved a generation or two beyond the initial oled screens, we will be back to having a stable usable product in another year or two.
To put it another way, if apple goes oled I would see about purchasing the same or a derivative screen. You will get 3-4 years of manufacturer availability on that as they wouldn't touch something they couldn't continue to milk as long as possible. Initial volumes will be VERY constrained by apple's purchases though, so that could make the first 6 months rather difficult to get product out to consumers.
TL/DR: Manufacturers need to learn to move faster and be in front of the electronics curve if they touch bleeding edge stuff.