I actually lowkey have a crackpot -emphasis on crackpot - theory that they might be ordered not to use CoC by their higher ups.
Basically a personality suppressant to make them be less rebellious to the WG....not a very solid theory, more of a shower thought as of now.
...Ayo, the psychic connection is strong. I had that shower-thought the other week.
It low-key makes a ton of sense: Sengoku refuses to use his CoC because he's been subservient to the WG, while Garp is Garp.
Also kinda ties back to Kaido going "we don't need that many Conquerors"...
If CoC is the God's Knights/Gorosei's greatest weakness, it makes a ton of sense why Imu wouldn't want Marines to have it.
I could see the CDs claiming CoC as a "Holy Power" only they should be allowed to use.
If they can forbid research into an entire century of history, they could easily ban a form of Haki, with the same explanation as the Ancient Weapons: it's just too dangerous.