What is a Haki specialist?
- They come in three types. Conqueror, Armament, and Observation specialists.
- Conqueror Specialists have a high proficiency or potential for Conquerors Haki.
- Armament Specialists have a high proficiency or potential for Armament Haki.
- Observation Specialists have a high proficiency or potential for Observation Haki.
"Adcoc" isn't a real term, the real term is Conqueror Coating, and the characters who use it most often are Conqueror Specialists. It is implied their ceiling for its use is higher than with Armament or Observation Specialists.
The confusion here happens because people oversimplify Conqueror Coating as just abundant haki instead of a specialized type of haki use. In that context, all of them can have high levels of mastery, but they're not all specialized in Conqueror type. World's Greatest Swordsman aligns with World's Strongest Armament Specialist terminology. Why should he have the strongest Conqueror type? He's not even a Conqueror.
IF Mihawk was a true Conqueror, he would be able to do things like 1) nullify Devil fruits 2) use Conqueror Coating on his body 3) knock out people selectively in a crowd, etc., but those are all Conqueror based abilities, so he probably can't do all of that stuff. These guys are only assuming he can do that, and that's a lot of assumptions.