I take the following to be the central question: “At what point did the evolution of "grammar" stop and all languages throughout time became as "good" as each other?”. The question contains a few important premises, one of which is that the evolution of grammar has stopped. In biology, the term “evolve” is traditionally used to refer to changes in heritable characteristics. Some linguists reject the notion that there is a heritable cognitive faculty of language (as distinct from general human cognitive abilities), and therefore it is not a foregone conclusion that “grammar”, specifically, has evolved in the biological sense. I don’t know of anyone who denies that there has been evolution of general cognitive abilities in hominids, so we might safely substitute “cognitive evolution” for “grammatical evolution”.
However, linguists tend to use the term “evolve” in a broader sense, usually simply meaning “change”. Using this broader sense of “evolve”, we can say that Modern English evolved from Old English, or American English evolved from various extant dialects of British English spoken 400 or so years ago. But that is not a change in a heritable characteristic of the species. If you compare a hypothetical and speculative “cognitive characteristics of hominini some millions of years ago” to modern human cognitive characteristics, there will surely be some heritable evolution. The question is, what is it and who did it affect? It is not know whether there have been any heritable changes to the human language faculty, during the course of human evolution. (By comparison, we know from the fossil record that there have been numerous biological changes in “humans”, whether that be homo erectus, homo sapiens or various extinct intermediaries such as h.s. idaltu).
Using “evolution” in the broader sense “has changed”, without the genetic implications, grammars are always changing, and the assumtion that evolution has stopped is false. Using the term to refer to genetic change, the premise that there has been evolution within the time-span of “humans” is unsupported. It is beyond doubt that there has been cognitive evolution in hominids, but there is no evidence that the basis of language has genetically evolved since the emergence of “humans” as distinct from other hominini. The development of the language faculty in its current form may indeed be the defining criterion by which “humans” can be distinguished from other animals.
We need to examine the premise that “modern languages had to evolve from something that was not as sophisticated and therefore (not) as effective at expressing ideas”. In the biological sense, this is probably true in that before there was human language, there were pre-human cognitive abilities which did not include the conceptual faculty of modern (or pre-paleolithic) humans. Human cognition evolved to the point that open-ended systems of concepts like “girl”, “boy”, “person”, “ape”, “tree”, “leaf” could be formed and manifested via distinctive sounds – chimpanzees still don’t do this. The conceptual faculty also developed so that propositions could be formed. When and how this happened is pretty much anyone’s guess.
It is not unreasonable to think that the first human languages had the general capacity to form a hierarchy concepts and to express propositions, and that there was little by way of learned structural baggage. We know that the order of words in an utterance is not genetically predetermined, and we know that morphologically complexity is not genetically mandated. We could therefore assume that the first human language had no polymorphemic words, and word order was free, so maybe Proto-Human sentences were like “girl tree climb” ~ “climb girl tree” ~ “tree climb girl” and in princple the messages might have been confusing. The adoption of a conventional rule “put the actor before the verb” and “put the theme after the verb” could have emerged and been learned by subsequent generations, without the need for any biological evolution.
As for changes in sophistication of language (genetic or otherwise), there is no objective measure of “sophistication”, indeed I don’t even understand what it means for a language to be “unsophisticated” as opposed to being “sophisticated”. There is also no efficiency metric for the expression of ideas. In Logoori, you can express very complicated ideas in a single word, for example rwávataakakʊ́ʊ́ndaamiɲɪrá which we require well over a dozen words to express in English – ‘when they (humans) did not make you curse for me, four days ago or further in the past’. Logoori is so sophisticated and efficient that you can say yaakadééka to mean ‘he cooked, this is just general information’ versus – with a change in the tone of the word – you can say yáákadééka ‘we have been waiting for him to cook, and he has finally finished the cooking’. Unfortunately, the language requires verbose story-telling methods to express the difference between ‘He bought a car’ and ‘He bought the car’.
The claim that earliest human speech did not have recursion is literally question-begging.