The basic plant science fact is that plants don't "flush out" nutrients. They are absorbed so they can become part of the plant.
A plant gives off oxygen, water vapor, and root exudates. No minerals leave the plant.
If you stop feeding a plant it will start to die.
If the plant has to get nutrients for it's reproductive organs (flowers) by scavaging the leaves, the flower you smoke is still gonna have those nutes!
According to fire science, white-ash/black-ash is all about moisture, so in our world that's the dry/cure. White ash is completely consumed fuel. The blacker it is the more un-burned vegetable matter there is - charcoal is the extreme "black ash" version. In smokables the moisture content, and it's consistency throughout the sample is what makes the white/black ash thingy.
As far as organic or not, I think there are some organic-ish powders available now that the apartment dweller could feed on a sack of coco and do fine. The difference is that both require opposable thumb people to mix stuff, and feed the right amount at the right time, for each strain, etc. is like being a cook following a recipe or a chemist brewing a pH'd mineral cocktail. The plant is gonna eat whatever you put in the IV, and if you miss something there's a bunch of full-color charts for that
I don't look at living soil as being in the bottle vs organic argument. Both of those people still wave their pH pens about with an air of superiority
It's more just making sure before the grow starts that there's enough in there for the plant to eat. When I water it's is things for the soil, not the plant.
Because the soil is "living" and the microbes are actively feeding the plant, they are the workhorse. The roots actually strip each microbe of the calcium they went out and got last trip, then they recode the DNA for the next trip to go get the magnesium or the nitrogen. This re-coding is likely why and how the pH thing works on it's own, since we know that certain minerals are absorbed better at certain pH's. The re-coding likely requires a box to be checked making sure the microbe has the proper pH to perform it's assigned task. The microbe "chellates" the mineral and makes it plant available.
My plants never starve, but I never tell them what to eat. They have the buffet and most eat responsibly LOL