You made that point in another context a month or two ago, and it resonated with me. Upon reflection, I think your use of the word space here is mathematically accurate, although it is considerably different from the usual usage in the color management world. I don't propose that the color management world change its terminology -- I think that would be an uphill struggle to win the hearts and minds of a ship that's already sailed (Excuse me, I love mixing metaphors). Maybe you could propose another word that captures your meaning?
I have no problem with saying, say RGB and XYZ, are color spaces, as long as it is understood that they coexist in a certain sense as depicted in the diagram below (CIE RGB and XYZ):
If this geometry is not realized then people make errors in color calculations.
For e.g., the matrix for conversion from CIE RGB->XYZ is:
0.48872 0.31068 0.20060
M = 0.17620 0.81298 0.01081
0.00000 0.01020 0.98980
Now take the saturated Red = [1 0 0]'. The vector length in RGB space is 1. However, the same color is represented in XYZ as M*[1 0 0]', and its vector length is now 0.52. Why the difference? Because, the correct geometry, as illustrated by the above diagram was not used. If that geometry is used then the vector length is the same.
Such things have resorted people to jump too quickly to non-linear analyses (non-linear spaces), using all kinds of strange profile measures, etc, in certain domains.