My response basically echoes what I have already argued in the OP: “If we aren’t able to articulate a reason for why God should be triune, then we have no reason to believe that God is triune.”
No man can define the blessed Trinity. The Church only reveals what Jesus Christ has revealed to our humanity.
God created man in His image and likeness.
Because God has revealed is presence to our humanity in three ways by His Essence.
This theological and philosophical pretenses involve what is the presence of God and what is the Essence of God.
No man see’s God’s True Essence fully and lives.
It is reasonable to believe according to both scripture and man being created in the image and likeness of God. That God the Father is revealed in His Voice who is being, God’s presence not Essence is revealed in His breath (Holy Spirit) that gives life to man since the beginning, and God has made His presence known by His living Word who is also an eternal personal presence stemming from (begotten) the True Essence of God.
God is known by His voice which comes from the Father, God is known by His life He can only give by God the Holy Spirit, God is known by His Word.
The Voice, the breath ,the Word of God are all distinct from one another in revelation to our humanity. Yet all three living persons are One God in Essence, divinity and eternal being.
Because God is God, every attribute of God is living and existing eternally and reveals His presence to our humanity as Father=Voice, Holy Spirit=Breath (in creation) and His Word = Which became flesh God incarnate in revelation.
Calling to mind that each of these living persons reveal God’s presence to our humanity. Yet in the Voice, the Breath and the Word, God’s One True Essence is hidden in each revelations of persons.
Why the Trinity? Because God who is Love wants to commune His Love to our humanity and to all of creation with His presence.
As far as God’s Essence is concerned, no one has seen or knows including the created Angels except the Only begotten Son who is God Incarnate because Jesus revealed Himself as God who comes from God.
This is the problem with Islam, they are holding with Catholic’s to the unseen and unapproachable Essence of God. But Islam denies God the Father who speaks, God the Holy Spirit who breathes life and God with His Voice and breath sends His Word to fulfill His Will to redeem humanity back to His presence in Love.
God’s Essence has never come down to us, only God’s presence is revealed in and through the blessed Trinity.
Those who deny the Trinity revelation, are never able to reach God’s True Essence, for which they slave for, but never will attain God’s True Essence, in fact Angels and demons fear to tread here.
To come into God’s True Essence where the whole Trinity is being, all three distinct persons from one another without division and without confusion being One God existing in Eternity, without space and time, yet God revealed His presence in Trinity into creation and time.
For all things visible came through and from God which is invisible in the Voice, Breath and Word all three being distinct from one another, but the Trinity is never divided in ONE GOD and no other.
When man reveals his heart and mind, man images the Trinity, by sending his word, from his voice and breath, all three distinct from one another, yet all three come from one essence of man and all three reveal the one man’s essence from His heart and mind, who is only one and the same living person, that is you.
Creation cannot reach God’s Essence. God reveals His presence to creation, in the Father (Voice), and the Son (Word) and His Holy Spirit (breath of life) because creation comes from the one God who reveals His presence and makes His presence known in the persons of the Trinity.
Faith is our hope, reason begins the path of faith for our hope.
The Blessed Trinity is a mystery, yet God does not leave us orphans, God makes His presence known to those, who do not blind themselves by rejecting His (revealed Trinity) presence from our flesh that holds to only a carnal mind of understanding and self pride, which denies the invisible Spiritual realities from which the visible creation came from.
Peace be with you
I hope this gives you a different perspective that never conflicts with what has already been said by Catholics here.