Thanks to Scott Martin for informing me about this thread.
The Gamutvision program (which I wrote) can answer many of the questions in this thread about printer color response and color gamut. I can only touch on its many features now. There is far more detail in http://www.gamutvision.com
Essentially, printer color gamut and response is a function of the RGB working color space, the rendering intent, and the printer ICC profile, assuming that the profile correctly represents printer response. And profiles tend to be quite good in that regard; if they don't represent printer response correctly prints look awful; such profiles are quickly rejected.
Rendering intents, on the other hand, don't always perform according to the textbook explanations. I wrote Gamutvision in part to explore how they really work. You can quickly change from Perceptual to Rel Col & back and see the precise differences.
Gamutvision lets you explore the effects of all three factors-- working color space, rendering intent, and printer profile. It has a staggering number of displays that allow you to view not only the color gamut (the extreme boundary of color response), but the response of unsaturated colors and color differences (Delta-E, Delta-E 94, and many more). Displays are in 2D and rotatable 3D L*a*b*, xy, and uv spaces. (Tonal response is also displayed.) "Chromaticity diagram" usually refers to the 2D xy "horseshoe" curve, which is an extremely limited and distorted representation of color response. Despite its popularity it doesn't come close to characterizing printer color response.
By examining profiles, you should see that going from 8 to 12 inks may have only a minor effect on gamut (Gamutvision calculates the L*a*b* volume)-- it may have more effect on highlight tonality, which is an important (and underappreciated) aspect of digital print quality.
About the only limitation of Gamutvision is that it doesn't work in native Macintosh mode. (It would be rather complex.) It runs very well on Intel Macs that have Windows installed.