Because kg is the fundamental unit of mass and kW is typically used for electric motors.

Same reason you wouldn't use m²/s³ even though that's also technically correct.

If "kg" is the fundamental unit of mass, then honestly, why isn't a gram referred to as a "millikilogram"?

Reminds me of the protest in the Shenanigans and Gimmicks part of this project: https://gre-v-el.github.io/Dimensional-Calculator/

You're thinking of grams and watts.

Kilo is an SI prefix.

https://en.wikipedia.org/wiki/SI_base_unit

"The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.62607015×10−34 when expressed in the unit J s, which is equal to kg m2 s−1, where the metre and the second are defined in terms of c and ∆νCs.[1]"

The base SI unit for power is the watt. The base SI unit for mass is the kilogram. Yes, this is dumb, but it's the way it is.

[1] https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochur...