The way I see it, and as shown in your post regarding the Amazonian Pirahã tribe, reason obviously came before counting.

The people created a language with a need for reason (communication), but with no real need (reason) to count. Apparently a person either had and did whatever, or had not and did nothing.

No real need to count people, since everyone was likely known. You either went hunting with Roger, Joe and Sam, or not.

No real need to count mangos, since you either brought home enough food, or too much food, or not enough food.

Recipes? You either cook it, or don't, or burn it, or cook it a bit longer.

The limited numbering system mentioned in the article might even have been used in a local gaming system for the high-brows of the society, like a local chess club, or even a touch of wizardry. No need to let everyone know exactly how to figure out how many more fish you need to catch for the big party. Becoming the go-to guy for the tough answers is sorta mystical.