The struggle with green diodes is inherent because green light is actually produced by filtering residual green out of a red diode.
This is an overly simplified and technically incorrect assessment - not just for today's situation, but in general.
There are essentially two ways to make green leds and both are currently used by manufacturers. Each has their own drawbacks and advantages.
The first is using a blue led with a phosphor on top that converts the blue light into green (wavelength shifting). In practice this results in a fairly wide bandwidth and the challenge is to get good conversion efficiency, but the advantage is that the high-efficiency of blue leds can be exploited.
The second approach is to make a pure green emitter, no wavelength converting phosphors involved. These are technically challenging to make
with high output/efficiency mostly due to problems with substrate and coating purity and homogeneity. Pure green led technology for low outputs dates back to the 1930s (conceptually) and 1960s-70s (commercially). They've been on the store shelves for decades and became available to the general public at very low costs in the early 1980s. Today's requirements are of course high output and efficiency, and lots of research is being done to overcome the efficiency gap in the green and yellow parts of the spectrum. The challenge is fundamentally the same for green semiconductor lasers, but the bar is a higher due to the higher requirements on material homogeneity and purity.
Hence, we currently have the option of fairly efficient, but wide bandwidth green leds (the phosphor coated type), or lower efficiency but very spectrally pure true green emitters. If, as a consumer, you buy a green led, you're of course usually not entirely sure which type you've got unless you either do bandwidth and efficiency measurements, or if a sufficiently detailed datasheet happens to be available.
