Why are 720 nm LEDs so uncommon?
I suspect the answer is that AlGaAs is an alloy with a bandgap between that of AlAs - 2.16 (which is indirect) and GaAs - 1.42 eV (which is direct). If there is enough aluminum, the resulting semiconductor is an indirect bandgap semiconductor, which means that to emit a photon, it must be coupled with a lattice phonon, greatly reducing the probability of photon emission, which would make a AlGaAs LED of short enough wavelength rather inefficient at emitting light, instead producing a lot of heat rather than light.