Except that this is doing things the hard way. Your "adjustment by eye" needs to simultaneously compensate for the characteristics of the camera, and the subjective adjustment you wish to achieve.
If instead you use a camera profile to transform colorimetrically into a standard colorspace, then your by eye adjustment is independent of the camera color behavior.
I think most photographers will find an accurate reproduction (even as a starting point for adjustment) doesn't look "photographic". And I'm not convinced that the controls in photoshop offer any intuitive way to re-matrix the transform. To do this, one would need to adjust hue and saturation to the image in LAB space or YUV space. Each control effects another and it's not a straight forward way to color correct an image. The camera manufacturers understand this and have developed their own matrix transforms to get to what they think is a good starting point for "Photographic" reproduction. And, I think that for most photographers, this is the best place to start. And of course, Adobe has their own versions as well in their RAW converter.
I guess what I'm saying is that, for most photographers, camera profiling is a rabbit hole best left for those who have found they have a special need for it.
I also say this as I've been doing some motion picture color correction and I've been exploring the "camera manufacturer's" standard matrix transforms, vs creating my own. To conduct my experiments, I've got a shot of a standardized DSC color chart that I'm working on, but, to really see what I'm doing, I need to view the image on a waveform and vectorscope. These tools are not available in photoshop or lightroom, and working on normal photograph with only a histogram, would be like throwing darts in the dark.