I'm not convinced as to the magnitude of the effect on color, yet. The Linear versus Film curve response is IMHO (or it should be) a tone curve correction that is more than a post processing curves adjustment. It should be a Luminance based tone curve adjustment that leaves color (shift and saturation) mostly unaffected. A great example of how it should work is the Intellicolor technology from Topaz Labs.
I'll do some testing myself with Capture One, because Linear response reduces clipping of correctly exposed files and maintains highlight contrast instead of compressing it, and that's why I use it almost exclusively. I'd appreciate it if you have some examples you can share that show the magnitude of the effects on color (but I'll do my own testing as well, so it's not that I'm lazy).
Actually I think it's a plain RGB curve in Capture One. But I'd be glad to be corrected on that. The reason I think it's a RGB curve is that the TIFFTAG_TRANSFERFUNCTION when export TIF with embedded camera ICC profile indicates that.
DNG/Lightroom has a special type of curve as defined in the DNG standard, which is supposed to have "film-like" increase of saturation when you increase contrast with it, but it's also prone to color shift. A pure luminance curve I think most users would consider looking too gray and dull, although color stability is good. Most expect color to intensify when contrast is increased.
RawTherapee is a great raw converter experiment with different curves. It has Luminance, RGB, Adobe's film like, and their own "weighted standard" which is my personal favourite, which is quite close to Luminance but not quite.
I don't necessarily think it's wrong with a simple RGB curve with color shift and all, as long as you design your ICC to work on that curve. If you want color stability with total freedom to select curves my guess is that none of the current commercial raw converters are particularly good at that. It has not been a design target for them, the workflow for "accurate" color is to make a custom profile tailored for a specific use case, ie curve and illuminants chosen and exposing correctly.
The reason I got into this issue through working with Lumariver HDR (we now in version 1.1.1 support Adobe's DCPs natively, and I'd like to support Capture One ICCs too to make it more flexible in MFDB workflows) and also contributing to RawTherapee (the upcoming 4.1 release will hopefully have support for Capture One and Leaf ICCs) both applications which find tone curves applied through/with profiles a bit problematic as they're designed to start with linear input.
For the luminance curve to work as you intend the ICC profile must be applied before the curve is applied, but that is certainly not the case in Capture One. As said with Adobe's DCP it is, but then their curve is only marginally more neutral than a plain RGB curve.
I have not made any screenshots, there's some work to do it so I'll see if I get around to make some.