Flatwound strings are even "dull" on an electric guitar or electric bass. I've tried it. If you want a "jazzy" sound without ringing brilliances - go for flatwounds. Don't know, what's the correct expression in English, we'd say "Draht" (= wire) in German for what is missing when playing flatwounds in comparison to roundwounds. I've put a flatwound-set on my Framus Mayfield Custom (thinbody semi-acoustic) for jazz/swing: that's a great jazzy sound via amplifier but you hardly hear the strings acoustically. I'm sure it would be similar on a CG.
Strings for violins, violas and celli are flatwound, of course, but you usually play with a bow. When playing pizzicato on a cello, the result is an "upright-ish" sound with very few brillances. Roundwounds would ruin the fingerboard pretty quick and I estimate that roundwounds would produce a harsh sound with far too many overtones when bowed.
There are polished strings available (e.g. D'Addario EJ51 "Recording Strings") which do not produce finger noises. They sound like roundwounds, but only for a short time (one recording session or one gig).
So we still have to wait for string manufactureres to square the circle.
The easier way is changing the guitarists and listeners hearing habits: From now on, it's forbidden to change strings for every CG player on earth. In 20, 30 or 50 years nobody will remember the sound of roundwound strings anymore and flatwounds will be the new state-of-the-art.
»Did you try the new D'Eadario DJ 46's?« - »Yeah, but they've got too many overtones for me, I'll stick with my Average hyper-graves 510 with rubber trebles«