This is a great primer. I used to work in this field, but not as a colour scientist.
> So why do we have so many different color spaces?
I think there was a missing piece here. Different representations of colour are useful for different things. I'm not going to give any secrets away but...if your trade involves finding out how close one colour is to another, then something that represents colours as points in space could make the maths easier. Then if you wanted to know if one colour was brighter than another, then something that represents a colour with a separate 'brightness factor' would make that trivial.