A profile or matrix is there already in the Adobe software; this is like a canned printer profile -good but can be improved.
Well other than using the Calibrate tab, that's yet to be proven. Even without the calibrate tab, plenty of users provide a color rendering they desire. So this goes back to the question of, can you or can you not produce the color you desire and is using the Calibrate tab OR some custom profile going to do much for you. I suspect the vast majority of LR/ACR users are not messing around with Calibrate. In fact while I did run this routine on my previous camera, I've found no reason to do so with my 5D. Nor do I have an issues getting out of LR what I want.
And this matrix sets the place where automation stops and the photographer's job starts.
If you wish, the Adobe profile is the equivalent of the native Epson printer driver - it gives excellent results, but someone with access to a spectro and software can improve the print channel or customize the rendering of a print to specific light.
A far better analogy would be, here's where the Epson driver starts WITH a canned Epson profile versus building your own. With just the Epson driver, yes I can get a decent print. Without either the canned or custom profile, I can't soft proof, I can't get the RGB values IN Photoshop to send to the printer etc. The profile(s) we have in ACR/LR are where we now stand with good canned profiles from Epson. You might be able to get slightly better results rolling your own but the vast majority of users don't need to. And, unlike printing, Raw conversion is about moving all kinds of sliders around to get a desired color appearance. You do that before you print, then you want "what you see to be what you get". In this context, we're talking about getting what you want visually from the Raw data.
In the same way, someone with access to a spectroradiometer to measure ambient light, and a monochromator to measure the camera's spectral response can significantly tailor the quality of the Raw rendering.
That would get us far closer to this desired goal of a scene built input profile yes. We're not there now. The current set of solutions is based on the false idea that if you shoot some target (with a gamut that's a far cry from scene gamut), that the dynamic range of the scene and target are the same, you someone fingerprint the way the device captures the color which is still scene referred and has to be output referred. At least with the above idea, you can measure the illuminate and items in the scene if so desired. And the profile here is capture specific, not a single (or better in the case of LR/ACR duel) profile that is supposed to fingerprint anything in front of the sensor.
Even still, its doesn't (nor will it) guarantee the user will not need to alter the rendering controls to get what they desire. No more than shooting a Macbeth with 4 different kinds of E6 film will produce either the same color appearance or the "correct" color appearance.