Original bright yellow was a good candidate, since actually no one looks like this.

Why should skin colour be specified at all? Why not leave it as an implementation detail? Yellow is the popular default choice, but it could very well be green, blue, pink, or anything really.

Why are the Simpsons yellow, yet the black guy in the show is black?

There's no "neutral" rather its just "white without specifying it"

Why should the Simpsons hold any relevance to emoji?

That is your perception. What is neutral is cultural, maybe personal.

why not let people just pick which one they want to use

I guess they could just support custom colours, but that seems like a needless complication—much like skin tones themselves.

Just use a font with the colours you like?

This map doesn't seem accurate.

Indigenous is a tricky concept in many place. Can you tell me who that map defines as the indigenous people of the following places:

England

Japan

Turkey

Sri Lanka

South Africa