I was going to say some things, but it looks as if Habeed has covered it pretty well, and said everything that I would.
I’ll add that LEDs aren’t quite monochromatic (although they’re pretty narrow), and that I once built a device using banks of LEDs of three different colors along with a “mixing chamber” to even out the effects of all three. The current to each different color could be varied independently, so that I could adjust them to get as close to white as I wanted. The light I got was a lot “whiter” than you get from those “white” LEDs that use a blue LED and a phosphor. It’s clear from the Wikipedia write-up alone that the 683 figure is only true for a green monochromatic source at the peak of the eye response curve. Since the luminous efficacy is meant to be a measure of how well light is channeled to the visible portion of the spectrum, with no “waste” in the UV or IR (incandescents put a huge amount there), the best results will come from sources that put more light out in the visible. And there’s no reason to restrict yourself to only three LED colors – you can use more to give yourself extra tweaking control.
Also observe that, although this is good luminous efficacy, this is distinct from the source’s energy efficiency. LEDs may be “cold”, since all their light output goes into the visible (unless you use UV or IR LEDs), but they still produce heat. I once saw an LED produce so much heat that it melted the solder of its leads, and broke its own circuit. The most efficient light sources are still fluorescents.