the material isn't really the cause for the lack of large leds.
large leds have only recently become possible. most led's no matter how large they are only have an element that emits the light about 1mm square. it stands to reason that the larger the emitter is, the more light it gives off. its true, however, the larger it is, the greater its ability to ABSORB light is, it reaches a point where the light level begins to drop off and becomes less efficient.
think of it as being a black car sitting in a sunny parking lot. the black paint soaks up a lot of the suns heat, it absorbs it, but at the same time, its freakin hot if you touch it because it also radiates the heat back out...it does both.
just recently a company called luminus developed a film that sort of acts like a one way gate for the light. that's the best way i can explain it. some of there led's emitters get up to 12mm square. thay are used in a lot of projectors, tvs, lighting fixtures etc. 8k lumens from a single led is impressive.
hope this answers the question.