OLED is still overwhelmingly Samsung and LG, but OLED demand only represents around 5-7% of total display demand.
Have you heard of BOE?
The recent ruling Samsung got from the US ITC is similar to litigation they are conducting globally against BOE.
In return you get "deep blacks". But photographers have been raising black levels since forever because it turns out it makes pictures more pleasant. So, uh.
Permanent burn-in will happen with static images, but it happened on CRTs too and those once dominated the world. As long as it is infrequent, it is probably not much of an issue. Newer OLEDs, such as Apple’s tandem OLEDs, minimize the issue.
I am not sure what you think your point about black levels contributes to the discussion. Higher black levels would only favor OLEDs thanks to their inky blacks.