Once they themselves had kids they would be able to teach them their imperfect version of recursive language. This probably continued and amplified over generations.
It's a pretty interesting case of nature and nurture combining. The mutation is a prerequisite, but largely useless unless there's enough "nurture" happening during the critical period.
The point here is that the archaeological record seems to indicate that it's like one day we simply 'woke up.' Whomever was fortunate enough to experience such a mutation first would have had a tremendous competitive advantage. The degree in intellectual advancement is such that they would have probably been significantly better at just about everything -- most importantly in surviving and spreading their genes. Now take this person and what would likely have been their vast number of offspring. They could effectively take over the world. And I suppose, in a manner of speaking, they did.
Either that or the kinds of artifacts we look for simply don’t last longer than 70k years on a planet like this.
Or, it’s just rare enough that, when combined with the cost of excavation and the fact that scholarship builds on scholarship, it’s just not the kind of evidence scholars are going to dig far past we’ll established boundaries to find.
Lots of possible explanations for the data.
Non recursive language does not allow you to give commands more complicated than "you do this", for instance saying "tell X to do this thing at this time in this location" is impossible without recursion. You might be able to get as far as "tell x to do this" since you are essentially just saying "repeat these words to X" but you have no way of providing context such as the time or circumstances when X should be told or when X should be told to perform the action. All organization and command would have to be done spur of the moment. There would be no possibility of planning in advance or communicating abstract concepts and thoughts to others.
Even a small group of people with this ability facing another group without it would have an overwhelming advantage, they could deceive, plot revenge, strategize, distract, and confound their opponents with their seemingly magical ability to know what members of their own group were to do and say before they did it. They could conceptualize solutions to problems that the others could not even begin to imagine. They could invent new objects in their mind and then execute those plans or tell others about them. They could create new words and concepts in language through combination and juxtaposition. They would quite literally be super-human, every one of them a Napoleon and an Einstein and a Da Vinci and a Shakespeare at once.
There is in fact a theory that language is a tool for thought first, and for communication only secondarily.
Take for instance Google's translation AI. It developed its own intermediary language which facilitated translation between languages and enabled it to even translate languages it had not specifically been trained on.
e.g. It had a "word" for dog that wasn't part of any existing language.
e.g. it could translate Spanish -> French even though it was only trained on Spanish -> English and English -> French