This is news to me. In the work that Jack Hogan and I have done so far on the relationship of overlap and SMI, it appears that SMI suffers when there is too much and when there is too little overlap. We have not -- so far -- investigated the direction of the errors.
Are you suggesting that in the computation of the optimum compromise matrix that reducing overlap biases the errors wrt the reference values for the training set in the direction of increased chroma?
It should be possible to test that, but before I do so, I want to verify if that's what you are claiming.
The experience I'm basing the discussion on is my work with camera profiling. Sensors that are low in noise and have a good amount of overlap are generally easier to control in the direction you want, compared to those that have little overlap, especially combined with high noise. The reason being that in the first case you always have good amount of clean signal in all three channels also in highly saturated colors which you can recombine in the way you want, and in the second case you have little to play with in one or two channels when colors are saturated. The problem with overlap however is that the signal difference between different colors are smaller, so it relies on that it is balanced with the noise level. With little overlap you instead have larger signal difference between similar colors, which is good, but the drawback is that the overall color response is more difficult to control.
This is a very broad description though, sure there is a balance somewhere. There is things like "too much overlap" and "too high sensitivity in the wrong places" that makes it difficult to make camera profiles, especially too strong blue sensitivity is something I have seen a lot of. I've only worked with older sensors when it comes to having less overlap, having a low noise sensor with less overlap is indeed interesting. One can really only know how this camera behaves until trying it out. What I reacted to was the marketing material showing this quite little overlap and claiming that as an outright advantage, when my experience from profiling suggests that it can be quite problematic.
Note that typical matrix-related testing of color response only test moderately saturated colors. It's generally in higher saturations you start seeing problems, when it's more clear that the camera "wants" the color to be in a certain way. Try to pull it in your desired direction and all related must follow (all the way into lower normal saturation) or you must make a strongly non-linear profile with potential gradient issues, or you simply ignore how the high saturation colors end up and just optimize for the normal range. Therefore I don't think that SMI is very telling, any modern camera has a good SMI value regardless if it has a response that is difficult or easy to control end-to-end.
I haven't really come up with a good way to actually test for "camera profile friendliness" other than actually making camera profiles. I guess a matrix test which include matching of high saturation colors, that is not just a MacBeth CC24, but something like X-Rite's semi-glossy CCSG, could yield some interesting results. The key parameter I would look for I think would be if it linearly can represent the same hue from low to high saturation, lightness and saturation matching is less important.
If a sensor is difficult to work with, what you end up with is one of the following compromises: 1) good normal color, bad behavior in the extremes, 2) robust behavior in the extremes less good normal colors, 3) robust behavior in the extremes, good normal colors, poor transition between the two, 4) robust behavior throughout the range with a look adapted to fit camera behavior end to end. The last does not need to be a compromise, it just means that hues are not necessarily made to be realistic but to match what the camera wants them to be. For example making blues more cyan, reds more yellow which are popular elements in a look. As Phase One has designed both CFA and profile my guess is that have optimized it for their specific look rather than for being flexible to adapt any desired look.