I'm not sure they had the luxury of a variety of foods in moderation. I think in early societies they fasted and then gorged when food became available.
Hunter-gatherer societies hunted and gathered by definition. They had no such luxury of a choice of meats, just "what was killed today" or "nothing". They would have had no such luxury of being picky about which of the edible plants they ate, except for not eating too much of the poisonous ones. It's only after a long time of mutual adaptation that any society can become so dependent on a single foodstuff like cassava or nardoo. And that gives plenty of time to develop the process of preparation, step by step.
When the alternative is starvation, one becomes open to trying new/dangerous things. Given a number of starving groups with only poisonous plant A available, let's say only one group stumbles on a sequence of steps that work while the others die off. The survivors pass along the knowledge that poisonous plant A can be made edible by performing a sequence of steps (even without understanding exactly why those steps worked).
So now the descendants of those survivors can transfer that knowledge (i.e. that a poisonous plant can be made edible) the next time a food shortage occurs and all that is available is poisonous plant B. Rinse and repeat over and over again through the centuries.
Over time, the substances that no viable process was discovered for get labeled as poisonous. So now your 'culture' has a list of safe foods, a spectrum of unsafe foods that can be made safe (and how), and unsafe foods.
I think when hunter-gatherer societies discovered cooking, they could have tried to cook unpalatable plants to make them easier to digest. Then they could've used cooking on poisonous food stuffs to see if it made them edible.
As new cooking techniques were unlocked, they could've combined them to make things even less poisonous.
Cassava is also bitter as hell to start. Most things that reduce that bitterness also reduce the toxicity.
As long as it doesn't become a primary foodstuff such that it will build up in your system, you don't need to get all the hydrogen cyanide.
However, any group that can get all the HCN out, will also be much better off when the famine comes. They will survive; the other groups will not. That's a powerful force.
