I think the DNG marketing has pulled you in! That marketing (or perhaps less nefariously the perception of that marketing) has made supporting DNG (the container format), and supporting Adobe Camera Raw Adjustments seem like the same thing.
The issue here is not at all the DNG format. DNG is just a container. If you open a raw file in ACR, adjust some sliders, and export a DNG then ACR will put a list of those adjustments in the DNG container along with the raw file. When someone else opens that DNG in ACR it will opens the raw file inside and sets its sliders according to the list of adjustments. But it sees them because the adjustment list was placed in the container, not because the container is a DNG. You can also use ACR, convert to a DNG container and use a sidecar of the adjustments. Convenient!
If ACR opened a DNG and and saw a list of C1 settings it wouldn't know what to do with them. So to do what you're asking C1 would have to translate settings made in C1 to equivalent settings in ACR.
Unfortunately "translating" and "equivalent" are competing concepts. Translating from one raw processing engine to another is like translating from one language to another. You can get good results by hand (just as you grade first in C1, then grade later by hand in LR to match it). But if you do it by machine translation you'll get - at best - rough results. And just like language there are some ideas that would be easy to translate, some ideas that can be translated in a rough but imperfect way, and ideas that are nearly impossible to translate with any real meaning.
Let's do a thought experiment about what it would take to translate all of C1's adjustments into ACR adjustments, so that those translated adjustments could be placed inside a DNG container and read by LR.
Easily Translatable Adjustments
Some adjustments are relatively straight forward. For instance rotation and crop could be translated perfectly from C1 to ACR. 1 Degree of rotation is 1 Degree of rotation in any software.
Harder to Translate Adjustments
"push 2 stops" seems pretty specific. But open a raw file in both C1 and LR and push it two stops in each program and you'll get similar but distinctly different results. Other examples of "harder to translate" adjustments include highlight/shadow, clarity, and vignetting. All seem to have relatively clear definitions but they are different at the nitty gritty level.
Impossible to Translate Adjustments
Some tools in C1 that are just not available in ACR. How can they make the RGB Levels tool compatible with LR when LR has no such tool? How can you pass on the chromatic aberration removal when the tool in C1 makes the tool in LR look like a joke? (not important for your work, but literally hours of work saved in manual retouching for some of our product shooters)? How can you translate the setting for Single Pixel Noise Reduction (critical for landscape/architecture shooters) when there is no tool for that in LR and the handling of stuck/hot pixels is very different between the two (IMO much better in C1). How would you translate Color Editor changes - one of the most powerful reasons to use C1 - when LR's color tools are very different and lack any equivalent of the "consistency" slider (huge for quickly tweaking aberrant skin tone)? How would you translate the dust removal part of LCC in C1 (you couldn't just put patches down on each piece of dust in LR because the dust removal in C1 is more sophisticated than that). Then you have the masking/layering which is quite different in both programs.
Basic Look - Different Even Before Adjustment
When you open a raw file in both C1 and LR you'll notice not even the default look is the same. Both programs start with the same messy raw data but every layer of math thereafter is proprietary. Intuitively you might think there is only one "true photo" contained in your raw file, but this is just not the case; the raw file is meaningless without the extensive, complicated, and proprietary math used to convert it into a pretty picture. So even the default rendering, even with a calibrated profile in each, is going to be subtly different. Like hearing two tenors sing the same song - even if you ask them to tune to each other and sing it "straight", without embellishments or adjustment - it still sounds different. Even if they wanted to neither program could match the other perfectly - it would be like Coke reverse engineering Pepsi's flavors and releasing it as "Coksi"; the math is Intellectual Property. The math is WHY you use one raw processor over another (or at least one of the primary reasons along with usability, speed, feature set, stability etc). The math is the program. So arguably the most important "adjustment" is the underlying conversion from messy raw data that takes place before you even touch a slider. This would be essentially impossible to "translate" to ACR (without processing to a TIFF or other final-image "cooked" format).
I hear this often. "Why can't I export the raw from C1 to LR and keep my adjustments?" What this misses is that the Adjustments and the Program are the same thing. The entire interface, the sliders, the math, everything, is created from the ground up. C1 is C1's Math.
Competition is good for everyone. It fosters innovation. I'm betting Adobe would have paid a lot less attention to Lens Corrections in LR4 if dXo hadn't carved out a niche with them. Nor would Adobe have bothered to improve the low frequency color noise it had in shadows of LR1/2/3 if it weren't for C1 v4 which leapfrogged them. LR4 has improvement Chromatic Aberration Removal, an area they have been behind C1 in for years (still behind C1v5 if you ask me). etc etc. LR introduced tethering late in the game and still has no where near the feature set to make tethered shooting the workflow option it is in Capture One.
Likewise I'm sure Capture One 7 will have some great new tools (or tool improvements) which leapfrog LR4. Should they wait to release those new tools only after Adobe has implemented them, to make sure that they can translate the C1 settings into Adobe settings? Or perhaps all non-Adobe raw processing developers should ask for Adobe's blessing anytime they wish to develop a new tool and then give the improvements back to Adobe to insure compatibility?
Because that's the ultimate implication. If you want universal compatibility in raw processing then you have to remove all competition and uniqueness. No competitive program can develop or improve any tool before Adobe. Adobe will do all the innovating in raw processing, and the the other companies can scramble to reverse-engineer those innovations, or buy them from Adobe, add them to their software and then match them up as closely as possible.
DNG is not the automatic universal compatibility that it's pushers would like you to believe. It is simply a known container.