It's not genetic. Family Lineage increases the likelihood but at the end it's also about people being born with qualities and ambitions of the king
You're not born with any ambitions though are you, let alone ambitions of a certain type.
You can potentially have CoC and never awaken it because you're a civilian with a desk job.
If we're talking about how someone awakens conquerors, Luffy awakened his by the impossible ambition of wanting to save Ace from being executed. Zoro's goal makes complete sense it would push him to awakening conquerors.
Sanji needing to become a King for Luffy's goal also makes sense as a motivation. Scopper is saying he needs certainty, meaning Sanji is not committed to being a King because he's uncertain.
So really he's talking about a mindset shift. It seems you really can be mentally nerfed. And your haki will be affected as a result. More so it's to do with having a wavering spirit, someone whose spirit who isn't wavering (certainty) is going to have stronger Haki I believe.
So when for example Mihawk truly believes he's the strongest swordsman, that certainty in and of itself could bolster his haki, the same way Zoro's ambition could bolster his haki.
Same with Luffy's certainty that he's going to be the Pirate King, that's why he keeps spamming that line.
This isn't the first time Scopper has mentioned something like this, when he told luffy about how he should use haki, apparently the more literal translation is something like "engrave the way you use your conquerors haki into your heart/soul" Since the term haki is built upon the Kanji for "spirit/soul energy" this is scopper telling Luffy how to shift the frequency his soul.
Which is similar to what he's asking Sanji to do.
Another example would be Zoro's mantra when he used sanzen sekai, he's telling himself there is nothing he cannot cut. Because Haki literally means "Supreme Spirit Energy" absolute conviction would bolster your haki.