Cree has already hit 300+ lumens per watt at room temperature and 1W power throughput, and are showing no signs of slowing. The problem with LEDs is not wave issues, but the Auger Effect where electrons recombine with the LED junction material instead of going through the electron hole.
However, CRI is still meh. For gem work, you want sunlight or incandescent, nothing else is acceptable because you need a true blackbody radiator. LEDs work fine for isolating and orienting stars, adularescence, schiller, and sheens, but are horrible for tenebrescent gems, some dichroic gems, and such.
Also, some LED-covered wavelengths are still utterly useless when compared to other sources. UVB LEDs at their best are only about 2% efficient. You might as well stick with a raw phosphor-less fluorescent tube with glass filters for UVC and UVA on it at that point, you'd still push roughly 30% efficiency.
Red LEDs are also still rather meh on the efficiency scale.
220 w/lm is theoretical max for a smooth spectrum of white light. If you get to choose a spectrum you can get much higher using green centered at 555nm. If any "white" light advertises close or above 220 lm/watt the CRI suffers. It means they're using light that activates the human retina better but isn't actually a pure white.
Lumens are calculated based on human eye response https://en.m.wikipedia.org/wiki/Luminosity_function
Looked at this way blue lights are pretty terrible. But if you look at mw of photons vs energy input deep blue LED's are close to 80% efficient.
Regardless of efficiency, the phosphor approach is more popular because it produces white light that's tolerable to use. Even phosphor spectra have peaks and valleys though, and evening them out usually reduces efficiency. The most common representation of this is color rendering index (CRI), which measures color accuracy. I think that's usually the right tradeoff, as a little less light with a broad spectrum is usually more effective illumination, but the market is driven by the mighty lumen-per-watt.
What does the phosphor emit? There's no "white" wavelength. So a more homogeneous spectrum?
An approximation of white doesn't work for reflections which is the main reason this method isn't ideal. Real world objects can reflect different wavelengths very unevenly so even if these sources appear white directly their reflections take on a variety of strange hues.
The phospor spreads out the peaks so the light spectrum emitted is smoother, closer to black body radiation which is the type of light emitted by the sun. Humans are wired for sunlight so this makes things look better.
R G B
_=============_
A surface that reflects the wavelength at “x” will look fully saturated and bright: R G B
_=============_
x
But now imagine a “peaky” white. The histogram has peaks at pure R, G, and B, but the other wavelengths are underrepresented or absent. R G B
_=_ _=_ _=_
The light will look white to the eye, and surfaces that reflect a wide spectrum will look relatively normal. But look at our hypothetical narrowly-reflective surface from before: It falls in between the peaks, and thus will have a washed-out appearance. R G B
_=_ _=_ _=_
x
I wish we could do the same with sound and cameras, a place where our efficiency is still laughable theoretically and compared to the natural human sensors.