As for brown not existing - do you mean that just for light or for pigment? Does the Chancellor of the Exchequer also not exist?
[flerdle] I suppose. I still think there is a difference between subtractive colours (ie pigment) and additive colours (ie light) in this regard, though I would also readily concede that brown is almost as much an absence of any other describable colour as black - which is perhaps why you don't see bluish browns, because brown is essentially black with less blue in it.
Consider - when you mix paint to make brown, you start with yellow then add a bit of red and a small amount of blue. Another option is to just mix red and green, but I've also made brown by starting with red and adding black. There has to be some blue in there to take the colour away from being orange, but not enough to make the blue distinct: the blue in brown is like salt in vegetables.
I should perhaps clarify that I am not actually all that attached to the colour brown, and only own one pair of brown shoes.