There are several factors that contribute to the LEDs cost. Your base
assertion that a p-n junction is a p-n junction is entirely too
simplistic. A simple p-n junction composed of a single p layer with a
single n+ layer and ohmic contacts will not generate a significant
amount of light due to self absorption in the thick p-layer and the fact
that the recombination is not well confined resulting in low efficiency
of conversion from electricity to photons. These types of LEDs are easy
to make by diffusion and thus not very costly, but not a lot of light.
A high output led requires a heterojunction design and most high output
leds utilise a double heterojuction design. What that means is a
typical high output LED will start with a P type electrode connected to
a P GaN layer connected to a P AlGaN layer connected to a N InGaN layer
connected to another N AlGaN layer connected to a GaN buffer layer on
top of some substrate (usually sapphire, but Cree uses Silicon Carbide).
The n electrode is connected to the GaN buffer layer.
The thicknesses of the layers have to be precisely controlled to get the
proper wavelength output and the proper electrical characteristics which
demands a very complicated epitaxial growth process. Additionally, all
the different layers require careful processing to eliminate the stress
between the different lattice structures to prevent defects.
The result is an epitaxial growth process that can have very low yields
and wide variations in performance across the wafer substrate. When the
wafer is cut into the die pieces used for the individual LEDs, the die
pieces are checked for output and binned according to how bright they
are. The highest performing dies are consequently a small part of a
production run which leads to the more simple equation that low supply
and high demand = high price.
Hopefully that gives you some idea of how prices can vary so much for
LEDs and why high output LEDs cost more.