OLED offers the thinnest displays currently available.
Unfortunately, they are not getting thinner overall. I check new tvs at bestbuy sometimes. Well, they stayed the same thickness for a long time.
You can buy a very thin led monitor today. There is simply no way you would be able to find an oled monitor with its thickest parts to be thinner than that of a thin led IPS monitor.
In a sense, thinness of OLED displays is nullified by their overal size with motherboard and other parts.
And that is sad. I always disliked thick older lcd tvs.
It is a bit strange that OLED displays are not getting thinner. Laptops did, phone did, tablets.
I would speculate they simply dont know how, right now. Must be the heat.