Haitz's law. In oversimplified terms, the doubling in output is roughly every year and a half. We've been following the trend since the late 60's. I think that the first commercial success was the scaling up from the 5mm to the Luxeon LED which allowed using LED's in handheld flashlights and making them acceptable alternatives to incandescents. Then we've seen progressive increases in output from the same die size for about 8 years now. Putting multiple emitters into a small area is another way to sidestep Haitz's law but it didn't really increase efficacy.
Well, if the only way Hait'z law can be obeyed is by increases in efficicacy, that can't continue for long without entering into perpetual motion territory.
The reason multiple dice woudln't apply is that output per unit area hasn't changed -- I suspect the law has to do with surface brightness, or output per unit area increasing progressively. Similar to how running huge arrays of chips in parallel doesn't qualify as a "Moore's law" improvement -- as Moore's law relates to the DENSITY of transistors.
I think the use of multiple emitters will continue at this point for fixed lighting (sorry flashlight lovers) since it's a cost effective way to increase output from a given area/volume comparable to the incandescent. I think fixed lighting is the largest market segment for LED's and flashlights will be along for the ride, not driving it.
For fixed lighting IMO the ideal is diffused lighting anyway, so multiple dice makes a lot of senes. Another idea would be to do things like separating the phosphor layer from the blue chip. I recall there was one company that was selling ceiling panel fixtures where the phosphor was built into the diffuser, and "backlit" by separate blue LEDs. That way, if the phosphor were to decay, or the user wanted to switch to a different color temperature, the phosphor would be separately replaceable, but the LEDs would continue to work. Separating the phosphor from the emitter is something that isn't possible with traditional fluorescent technology, beucase of the danger of free-floating 240nm UV unknowingly sunburning the crap out of everyone's eyes...
I believe there still is a purpose for throw even aside from flashlights, so single die LEDs will necessarily need to improve in order to be adopted into general lighting as well. For example, things like vehicle headlights, and small spotlights (necessry to compete with small halogen spots) will require single dice.
Have we reached the peak from max outputs from a single die that they are now using multi dies like P7? Will the future brighter LEDs all be multi die types?
There isn't really a theoretical peak to single die output power. There is a practical limitation primarily due to heat. The main theoretical limit is 100% conversion efficiency of electricity to light. Right now the best blue LEDs are around 40%. Going frm say 20-40% efficient (The previous generation "jump") saw a huge jump in light output, but relatively little change in heat production -- most the electrical input is still turned into waste heat. As 100% efficiency is approached, the amount of waste heat to manage will decrease dramatically, thus allowing more power to be crammed through a tiny die without causing it to overheat. consider somedy in the future a jump from 80-90%. In terms of efficiency, that's a small jump, but waste heat production is halved.
. However, there is a practical peak due to things like heat buildup and resistance.