So as you refered to Rayleigh's Dialogue about Conqueror's Haki i feel as you omitted an important part where it says that CoC
can grow as the individual's personal growth.. And it ties to the point you made about being born with it due to family genes and their lineage..
It's not so much that the Lineage or Being Naturally born with.. But it's related to the Caliber of the Individual..
It says '' Lifestyle '', but i can tell you it's a poor translation.. What Luffy refers to there is the '' Caliber '' or the '' Worth '' of an Individual as a person.. That Usopp has Kuro beat when it comes to the Caliber of a Man and Pirate..
Being born with the right genes won't make you a de facto Conqueror but it will increase the likelyhood of having it based on the Caliber of your lineage.. An example of that is Koby, His Caliber as a person grew tremendously from interacting with Luffy and being inspired by him.. He's on the right track to grow his " Worth '', his " Character " as a human being to the level of a Conqueror.. I think that's how it works..
Caliber <=====> CoC
My second point is related to the ability to " Overwhelm " others, to have the Will of a Conqueror..
Zeff mentioned in Baratie that Luffy's weapon is like an unbreakable Spear and defined it as a '' Conviction, Faith or Belief '' to not fear Death..
Obviously this is another poor translation..
Zeff is basicly speaking about Conqueror Haki there.. I think to attain the Power to Overwhelm others, you need to first Overwhelm Death itself.. And it's what Zoro has shown early in the series.. To go beyond a state where it would normally Kill someone.. THat is when he was tied Starving for 9 days at the Marine Base.. Well he sort of cheated by getting food from the little girl, though he demonstrated the Spirit to Overwhelm Death there..
Or Oden being boiled alive in a pot for an Hour.. That would be CoC and the power to Overcome Death for a While..
In the Fact, the way Zoro unlocked CoC is precisely because he chose at that time to Overwhelm Death itself.. Declaring that if he kept unleashing this much Haki it would Kill Him and realise that Yes, it's How it should be to achieve Enma to Stabilize he had to Overwhelm Death.. And go beyond the Realm of living things..
Chapter's 1036 Title is directly related to this and how Zoro got CoC, that Bushido and Death are interconnected..
The translation says " Bushido is the Way of Death ".. Again not quite the right translation but it gets the message across..
Cause the Japanese line allude to, the concept of Bushido being Death and Finding it?.. It's like a phylosophical sentence which
i understand why it would be hard to translate that to a hundred percent accuracy..
I think i had another point.. But these were my 2 Big Ideas..