Although in the case of chromatone, I don't see any arguments made about technical improvements. Instead of spelling note names with letters, we have colors. Why is this better? This some argument about the visible spectrum mapping. But like, how is that useful? I can tell a group of working musicians "1-4-2-5 in E minor", and we'd probably be able to play something moderately coherent based on that. How do I do that in Chromatone? What's the advantage?
Most people (aside from those with perfect pitch) experience pitch relatively. Things like intervals or scale degree given a tonic. Maybe there's something interesting one could do mapping colors to something in this domain, a la solfege, like a minor 9 chord becomes green or something. I'm still not totally sure what the point would be. Maybe you could read a chart quicker.
But like, what's the problem in traditional notation/theory that we're trying to solve here?