On the other hand, Doflamingo said that Luffy has greater potential than Law due to having CoC, which implies Law doesn't have it. Unless it is hidden and only recognized when unlocked.
It is clear that Doflamingo was wrong about Law, completely.
Throughout PH and DR, we've seen Doflamingo consistently making misjudgements to Law. Either when it is about Vergo's Haki being enough to stop Law's hax or when Doflamingo thought Law won't pull out anything else - boom, his organs got shredded by Gamma Knife. Luffy dealt the finishing blow but Law's Gamma Knife was another crucial moment why Doflamingo lost.
Furthermore, if we consider the fact that Doflamingo was already making a conclusion on Law's potential based on the lack of CoC, his conclusion already failed miserably when Law awakened his DF a few weeks afterwards.
So it isn't wrong to assume that Doflamingo was wrong about Law's inability to possess CoC as well - because he hasn't unlocked it yet.
Kaido only felt Zoro's CoC when his CoC was leaked during his Asura attack (and no Z bros, Asura was coated with CoC).
All the big shots only knew about Luffy's CoC when he was using the fodder control by accident in MF.
As for Law lacking enemies EoS - there are literally 5 Gorosei and it isn't clear if Imu resurrects top tiers from the past.