TL;DR: According to Christianity and the experience of saved people TODAY, what fallen (non-saved) people consider "primitive" and "common sense" is no longer the same as the people in the original state of purity and innocence. So to answer your question, it depends on who you ask. To believers Trinity makes more common sense, but to the fallen / unsaved, who can predict what their corrupt reason say?
The fuller answer below is for Trinitarian believers who want to defend that our concept of Trinity actually explains more of the true nature of the original / redeemed human heart.
I'm in no way saying that just by having "common sense" people can discover Trinity on their own without God's history of revelation recorded in the Bible. But after their reason has been "baptized" Christians should recover the original state of purity and innocence and only then will they discover that Trinity makes more "common sense".
Christians believe God created human being in a state of purity and innocence. What does it mean? It means that the human heart, through experiencing the world in what we are doing, thinking, and making is longing to relate to God. The mind wants to glorify God. The emotion is naturally overflowing with joy when contemplating the beauty of God's creation. The body wants to give what we create to God as an offering, like a child who like to show her art project to her daddy, who thanks her daddy for supplying her with crayons and art paper. That is the state of purity and innocence which the doctrine of Trinity tries to restore us to.
But we live in a fallen world. There is a deep shadow obscuring this purity and innocence. Human beings now want to make our own God, by making our own ethical standard of right and wrong, and by casting God in our fallen image. So what's common sense for unsaved people should be taken with suspicion.
Trinity does not cease to be Monotheism. There is still one God and one Universe which does not contain the one God. But is this conception sufficient to capture all the longing of the human being created in the state of purity and innocence? There is no inherent relationship in having one God that is aloof from creation, the "watchmaker" God created by the fallen enlightenment era philosophers. Even Plato's demiurge + world soul was better, and Neoplatonism was more satisfying as a religion compared to the modern solitary conception of human as orphans entirely "trapped" in our individual body unable to relate to each other and to the creator. Very sad and tragic ! What Trinitarian conception of God brings is to "relationalize" this Monotheistic God unfortunately mangled by philosophers.
It's a logical fallacy to insist on being able to explain the "logic" of the Trinitarian "One God in Three Persons" before you can believe God as Trinity. Even the Monotheistic God does NOT have to be fully explained in order to be believed, so why compare the more difficult way to construe Trinity to a simpler "more primitive" Monotheistic conception that could very well turn out to be less than real? We need to learn from the more humble Aristotle and Plato who acknowledged some unexplained aspects of God rather than the modern philosophers who at the end of the day reduce God to what they can define. I hope you see the arrogance and absurdity of some philosophers who value logical consistency more than reality. On the other hand, philosophers like St. Aquinas or St. Anselm realize the limit of their philosophical endeavors and by faith see within their hearts the reasonableness of Trinity because they have a more pure and innocence concept of reason. That's why the medieval philosophers see philosophy as a handmaiden to theology as opposed to some modern philosophers who see theology as an obstruction or myth to be destroyed.
Christians believe that by having Holy Spirit in our hearts we are able to participate in the Trinitarian love relationship within the Godhead, following the example of Jesus who while being fully human was able to live this state of purity and innocence before God the Father and having the Holy Spirit in His heart. That is why in order to recapture the pre-fall state of human heart we need to follow the example of Jesus.
We can start by acknowledging him to be the Son of God, the first step to see this Monotheistic God as a Trinity.