Until it gets to the RAW converter how would it even know what the target colorspace gamut is? What kind of compression does C1 do and what assumptions re gamut does it make?
Exactly, that's why I don't think it's particularly good design to make it in the profile, but that's what's "everybody" does, and raw converters have as a result limited control of large gamuts and thus makes it harder to work with profiles that doesn't compress a lot, when you shoot high saturation subjects.
The assumption seems to be that target color space is something similar to AdobeRGB, but there's not really a fixed target gamut, it's more like "with proper handling of clipping it should look good in AdobeRGB sized gamuts". Compressing camera gamuts is quite different from screen-to-printer gamut mappings, as with the camera you don't really know what you're going to get. Few "real" colors trigger a raw response of 0% R, 100% G and 0%B for example, so the outer limit of what the camera will deliver is sort of unknown. It's popular to say "camera's don't have a gamut", and this is one of the reasons.
Another aspect is that cameras can deliver very saturated colors, far outside AdobeRGB. The amount of compression required is typically much larger than regular gamut-mapping tasks, so you need to apply different much more subjective methods rather than just using colorimetric formulas.
I can't describe exactly how Capture One does its gamut compression, as I don't know. I haven't really studied it in detail, I try to come up with the best method I can do based on own research. I do look at Capture One and Hasselblad etc for sanity checking and compare performance. One thing I can say though is that to achieve higher compression you don't only work along the saturation axis, but also lightness, darken saturated colors to fit in gamut, and lighten saturated shadows (as colors can clip to zero too, not just max value). Evenso you must still consider scenarios when the camera does clip, like sunsets. "Mathematically accurate" gamut compressions make sunsets and other scenarios involving clipping look dull.
Making pleasing gamut compression for cameras is a little bit like making pleasing skin tones. It's not so much science, but more trial and error and judging the result by eye. It's not about putting the camera into a fixed gamut range, but to dampen the outer range so it behaves a bit "nicer", so when you shoot that deep purple flower you don't immediately need to pull lots of sliders in the raw converter to reduce clipping into reasonable levels, but instead it provides a pleasing output without adjustments.
As I've mentioned many times, camera profiles are still today intended to work as a "film roll", it should provide a well-behaved look within a reasonable gamut without requiring further adjustments of the raw converter, automatic or manual. It's not the way I'd like it to be, but it's legacy from the analog days and it's not going away soon.