I have spent 10 years studying color science. I know what color temperature is. I’m just explaining why the moon is a poor analogy. I have an issue with bright short-wavelength light sources at night, regardless of lamp configuration. It knocks out night vision.
There is a wide literature (dozens if not hundreds of research papers) on this topic. It’s not exactly some deep mystery.
The lamp configuration just makes things worse (and the use of fewer, brighter lamps provides much of the economic incentive to install the new lamps, along with federal subsidies).
That is a problem that LEDs could enable (by making very bright lamps available) but is not really a problem of LEDs but a problem of using any bright light source wrongly.
My understanding is that the use of lower-energy and more durable light sources provide most of the incentive to install new lamps. I.e. electricity bill is lower and you need to change the lamps less frequently which reduces maintenance cost.
This makes the installation cost more attractive to the city.
The electricity bill is (potentially) lower if you replace very old lamps with LEDs at the same brightness.
The best sodium lamps are quite efficient though, so LEDs have only marginal advantage compared to replacing the old lamps with newer sodium lamps. If you make the LEDs dramatically brighter, then they actually end up using more electricity.
I haven’t seen any especially convincing numbers about an LED lamp project that saved on electricity bills. I’m not an expert in the subject though, and I haven’t looked too deeply into digging up data.
As others have noted, we sleep poorly under strong moonlight.
I live in a very rural wooded area, and I can leave my blinds open except when the moon is at its brightest -- I sleep very poorly if I don't use blackout curtains.
Perhaps the fittest humans were the ones who stayed the most awake and aware of nocturnal predators during the brightest nights of the month?
You are confusing color temperature with how the lights are installed. If your streetlights were 4000K and spaced properly you wouldn't have an issue with them. The penny-pinching distribution (high lumens, wide angle, distantly spaced) of lights chosen by your city is at fault. That layout will create maximum glare and is the most miserable layout imaginable since distant lights will always be shining directly in your eyes.