This point does hinge on your description of how we came into language (why I mentioned there are stakes involved in the 'uptake' into language... why I didn't want to go into it in the original comment, since it's a more lengthy discussion).
I mean, yes, if you view language as a piecemeal, natural evolution (saying 'berries!' is better than grunts, so those who learned to say 'berries' survived), then on the surface I would say you are right. But that's rationalist, rosy view that just makes common sense, so everyone kind of accepts it... I think it's a pretty big oversimplification. There are plenty of anthropologists (at least when I studied it back in college) who talk about it as a much more sudden rupture, exactly related to the increased vulnerability of humans at birth (we are the most vulnerable species for the longest period of time after birth), which itself coincided with a mutation related to skull size and skull malleability. From this angle, introduction to language is mostly a side effect of the vulnerability, and took place as a relatively dramatic cut. It's almost like entering into a different realm, with it's own rules/ effects that weren't tempered and shaped by evolution/ natural selection over a long period of time.
I mean, the truly evolutionary advantageous thing would be don't give humans self awareness and consciousness like we have it, self questioning, free will and all (and yes, we have free will... I won't get involved in that argument) ... instead just have them act like animals/ automata who do more complex things and speak words. The fact that we have all these complex mental states and behaviors which don't seem to have any apparent evolutionary purpose whatsoever, I think further supports this view of language/subjectivity/consciousness not as something tempered and forged by evolution/ natural selection gradually, over a long period of time.