I'd love to make more contributions with demonstrations and further dig into how C1 does its colors, but I don't really have time with that. The only reason I've dug into it this far is so that my profiling project can produce profiles for it. It's time consuming to do this kind of stuff, and now I'd rather put that into improving my own color profiling engine.
Anyway here's a short one on the color correctness of Capture One. I don't have an IQ180 shot of a subject of to me known color, such as a color checker, so I can't compare for IQ180 specifically. But for demonstration, here's an example from a P45+:
First Capture One's default profile result:
Then a calibrated result:
Both with "standard film curve" applied, the calibrated profile is generated by an in-development DCamProf using it's "neutral tone reproduction operator" whose purpose is to maintain color appearance over changed contrast (increased in this case). Feel free to compare to your own color checker.
My own observations of C1: dark blue is much too bright, the left orange is more yellow than the actual orange, overall saturation is a little bit too low (with exception in the foliage range for example). Those are the larger errors, there are smaller too.
The DCamProf result may be a tad bit high on saturation, but overall the color appearance match is a ton better although not 100% perfect. Doing a side by side check with a calibrated monitor and a real color checker under sane light should make this obvious to anyone.
Now there are reasons why C1 has made the colors like that. That dark blues are too bright is probably because they have reduced or even skipped lightness corrections, as that can in some circumstances negatively affect gradients, and lightness errors while easy to detect in a side-by-side comparison they're least objectionable and hard to detect if you can't do a direct comparison with the original.
While lightness errors is probably largely due a side effect of hardware limitations, the hue errors are most likely designed. I've noted that skin tones are often made less yellow than reality for example probably because many think that's more flattering. More saturation in the foliage range may be a landscape adjustment. Why they have brought orange and yellow-green so tightly together I don't really know. It could be a side effect - sometimes you increase color separation in some color range, but that means that you must decrease it in some other.
Note that I do not believe that the most accurate color means the "best" color, but I do believe that maybe it's not to the photographer's best interest that the manufacturer designs looks for them. Maybe the photographer should herself/himself be more in control.
During my work with camera profiling I have noted how easy it is to "fool" oneself and think, "wow - this looks really accurate", for example if you shoot a subject in one room and look at a screen in the next. When you bring up the possibility with side-by-side comparisons you note that the bundled profiles are not very accurate at all. This does say though that color don't really
need to be accurate for most applications. It has made me very skeptical about various claims of "accurate" color out of the box though. We see things we want to see, and the eye/brain is very forgiving and good at filling in.
The P45+ is an old sensor which has less overlap of color filters than a more recent like the IQ180. This means that it's easier to make saturated colors with less noise (good as the sensor is a bit noisy too), but harder to separate colors. With increased signal-to-noise ratio color filters can now be more overlapping allowing finer color separation capabilities, at the cost of noise increase when making saturated colors (which isn't as harmful as before due to the better S/N ratio). Most differences you see are designed in the profile though.
I'd love to see a similar comparison made with an IQ180, I think you would get a similar result, that is a perfectly alright realistic look but with a few quite obvious color errors that for various reasons have been designed into the profile. So forgive me, before I see such a demonstration I cannot really trust anyone's word that the bundled profiles provide accurate color.