My experience building ICC camera profiles over the years has been hit or miss. With the right target, lighting, software, raw processing software and the stars aligning properly, in studio profiles are doable.
But ICC camera profiles have one severe issue, they are output referred. The path Adobe took with DNG profiles (which does limit their use in their processors) makes a lot more sense and work pretty well. IF I were using C1 I’d be looking for them to sort out the secret sauce in their processing and hopefully supply good profiles with perhaps some tools to tweak rendering to produce a desired appearance.
The biggest issue with ICC camera profiles is the idea you can treat a raw capture like a scanner.
You can make ICC profiles work with cameras, just ask Jack Holm. The output-referred argument was an expression of Thomas Knoll's NIH attitude, I had this discussion with him.
Profiles work so well with C1 that they asked me to make some some years ago, when a lot of Leica users were using my profiles. But they were not very friendly buisnesswise, they refused to take legal responsibility for the product, and when I realized they were involved with Microsoft I bailed out because of other small developers who told me their life became hell after they did business with Microsoft. I used to be a computer journalist.
Raw developer also uses ICC profiles to good effect, I believe.
I had a custom camera profiling and editing suite with some tools I wrote myself.