Humans, like beasts, can express themselves without using language, and they do. Humans probably have a richer repertoire of postures and faces than beast do, to express anger, to challenge, to convey amorous disposition, boredom and many other mental states.
You can limit yourself to that if you want to. Me, I value the possibility we have of using an articulated language.
We can speak by making groans and shouts, and we do. Some people do more of that than others. Humanity at some point in the past must have been limited to that. Thanks God, we're not longer.
I'm old enough to have seen language evolve. Between 1995 and today, I saw how British English changed. I myself sound as if coming out of an old French film! Language evolves because it is a tool we use to express our ideas and our ideas evolve with our culture. A civilisation using books to record its ideas will evolve differently. 2,500 years after he put his ideas on paper, we can read Aristotle and continue arguing about his ideas.
The quantity today of the information somehow processed by humans and available to them on some material support external to their own brains has increased beyond anything even Aristotle could have imagined, let alone foresee. We cannot ourselves even imagine it properly. Maybe a metaphor for it would be the size of planet Earth.
Languages do not follow rules but present regularities. Different languages may be thought of as different plants growing in different regions and climates. Structure is functional. A given structure allows speakers to exchange ideas up to a point.
"Shut up" has neither subject nor predicate and yet we use it to effect. However, relying only on injunction would be a limitation of the semantic of our conversations. The subject-predicate structure offers more possibilities. We use it today because our ancestors opted for it at some point and it turned out to be very convenient and full of potentialities.
Marie loves Jack. You can say it using the subject-predicate structure, but at some point, without even being aware of it, humans started to think of it as subject–verb–object. There are languages favouring the SVO structure, while others prefer the SOV structure. However, according to Wikipedia, SVO is "the most common order developed in Creole languages, suggesting that it may be somehow more initially 'obvious' to human psychology".
Languages differ but there are all subject to the same physical constraints and they all are used essentially for the exchange of information and ideas between humans. And exchange of information and ideas are critical to the individual as well as the community.
Thus, structures that are efficient will be retained if the community has a need for it. Structures that are more complex have a cost: more difficult for the speaker to control, more difficult for the audience to understand. Cost and benefit. Languages evolve with the culture and therefore the civilisation.
The subject-predicate structure is not absolutely necessary but it is very convenient, very efficient and full of potential, even taking its cost into account.
Maybe we could have a look at mathematical and technical languages. Software languages are probably a good indication of the range of possibilities in terms of structures. And of how useful it is to avail oneself of these structures. Or indeed how costly.
Logic and language. Language is only the vehicle. We do logic without realising it and without formalising it. Language and our use of language reflect our logic, which explains that Aristotle could notice and that he was able to observe the empirical facts of logic by looking at how politicians and philosophers argued, i.e. how they used language to express their logical ideas, logical ideas they didn't even know were logical.
Aristotle described what logic would come out of the language he knew and of how people used it. However, logic is much more primitive than language and more primitive languages will be just as much used to express the logical ideas of the speakers, however primitive the language or the speaker.
We can get people to do what we want using many different ways and, between the whole of us, we use them all. Brute force. Cajoling. Insistence. Command. Argument. Well, I will assume that argument proved decisive to the civilisation inherited from people like Aristotle. Democracy is founded on the modality of argument and it has been a long journey. And we are still on it. Did we find anything better than argument yet?
But nobody is forced to argue anything. We can listen to music, which is another kind of language, perhaps.
Yes, the logic of the subject-predicate structure, like the logic of any structure, leads to infinite regress. However, we stop the regress as soon as we can agree between ourselves on what exactly are the facts of the matter. Which is why we usually don't need to argue with ourselves, and why, like sex, we need to do it with other people.