One problem with that approach is that in the HR diagram the absolute magnitude is not a single-valued function of the B-V colour, as you point out yourself. While it is true that dwarfs are much more abundant (per volume) than super-giants, the giants are much more luminous so they are seen much further. Thus we actually
see about as many giants as we see dwarfs (you can check that in the Hipparcos data; I strongly recommend you to have a look at chapter 3.5 in the first volume of the published Hipparcos catalogue: "Statistical properties: Astrophysical Relationships". If you don't have access to the hardcopy, you may check out the online 1.6 MB
PDF file or the 875kB
PS file. I think you will find it interesting.).
The difference in magnitude between red dwarfs and giants is between 5 and 10 magnitudes, so the distance will err with a factor of between 10 and 100 if you pick the wrong luminosity class.
I've been thinking of implementing another, slightly more advanced approach in
StarStrider. You see, even if the GAIA parallaxes are more or less useless for direct distance determination, they may be sufficiently accurate to discriminate between the luminosity classes. Then one may use the B-V (or other) colour to better nail down the distance by deriving a representative luminosity and assuming zero extinction. The distances will be rough, but maybe not useless.
In detail, I think the following procedure could work:
1) Determine a colour/magnitude relationship for dwarfs and giants using Hipparcos statistics for stars where the luminosity class is known.
2) For a Tycho star, use the colour of the star, estimate its luminosity from the Tycho parallax and visual magnitude, and assign it the luminosity class to which it is best consistent. [You may also determine the confidence and
how consistent the assignment is, to reject bad fits].
3) Use the relationship from 1) to determine the luminosity from the colour and luminosity class.
4) Use the luminosity to derive a distance by assuming zero extinction.
From the Hipparcos statistics in step 1) you can estimate the error of this method. With more than one colour (e.g. V-I in addition to B-V) you may also estimate the extinction, but that is more advanced.
(extinction is a measure on how much the star light gets fainter due to non-geometric effects such as scattering and absorbtion due to interstellar material)
You're are welcome to implement this method. It will be some work of course, but I'll be happy to help you if you run into problems and will be interested in your results. And so will the rest of the Celestia community I presume.
/Alexis