actually alot of ppl get it wrong, the higher the temperature does not mean the brighter it is. Maybe exterior wise yes, it is because it is more eye catching colour (for example: 6000K = Pure White; 8000K = Blue-ish White, 12,000K = Purple).
But in physics theory, the higher the temperature means the lower the lumen. So the wavelength of the beam pattern is also shorter which means lower visibility. Actually in my opinion those 10,000K or 12,000K temperature is for 'look' only, when driving at night especially rain the visibility is really poor. See below the table of temperature vs. visibility. My practice is don't go above 6000K for best visibility.