Theologically speaking, there has been a trend spanning more than a century toward a "social" concept of the Trinity within the church, be that Catholic, Protestant, Evangelical (although patchy), and even Orthodox. What this means is that the Father, Son and Holy Spirit are understood as three literal persons, in a way we would understand personhood from our own everyday experience. Each has a first-person perspective, a will, a uniqueness, all covered in an unsearchable love and submission in the most perfect of social communities. Dr. Stephen Holmes is quite vocal about the problems with such an approach, which sometimes favours distinction over a united Godhead of precisely 1. Today I will try to describe a paradox I notice within the social-Trinitarian "move".
First, I have a silly illustration to try to show how the social Trinity vision is inappropriate to the Biblical presentation of God and Christ.
You want to talk to your Heavenly Father about something. Can you ask Christ or the Holy Spirit to leave the room? Impossible. We are connected to the Father uniquely through his Son: on this all Christians should be on a similar page. We can't have a private conversation with our heavenly Father and say, please, Jesus, I'm ever so sorry, but would you mind just stepping out for a few minutes while I share something on my heart with Father? He can fill you in later if necessary...
There is a very deep connection that social Trinitarian offerings need to explain more fully, if their "divine persons" can truly be understood like persons as you or I understand personhood. Can you think of any human parallel where a son has a deep connection with his Father while having to communicate via an older brother (I know that this 'via' could and should be discussed at much more length)? Nope, that kind of intermediary would usually add distance, not closeness. So inseparability of Father and Son should be an issue for diehard social Trinitarians, because you cannot ask Jesus to leave the room. Some antitrinitarian Unitarians would also likely be tested by this line of reasoning, but John's gospel in particular, I think, requires it.
Now I don't yet re-believe in some kind of divine "essence" or "substance", and I do not think it likely that I ever will on general grounds, because I don't think things have essences. My table does not have "tableness". My phone does not have "smartphoneness" or "Huaweiness". My table is a table because it has properties that speakers of English can agree fit the item. My phone is also clearly a Huawei smartphone. Even humans, I would argue, do not have a human essence per se. We are humans. By saying "we are human" rather than "we are humans", we hint at a distinction that has had implications for Christology in the past - distant past, but not 1st-century past. This kind of language is fine, but you need to realise what underpins it. Scientists examining a newly discovered bug in the rainforest would not exclaim: "it is spider!" They would say: it is a spider! Creatures only tend to lose their articles when truly we talk of their meat!
Divine isolation is ruled out through relationship (which would be the only possible avenue for developing substance/essence theories as far as I can tell). If I'm right about Thomas' declaration (see my post on this interpretation here), then Thomas is not speaking of Jesus in isolation from his (their) Father. He sees the Father in Jesus. Those who presuppose the existence of some kind of divine substance might be less inclined to notice this, for they hunt for passages that speak of Jesus in apparent isolation from the Father, and say: look, Jesus is God!
So here I see here a paradoxical perk in some strands of social Trinitarian thinking, because while this kind of deep mutual indwelling is underemphasised in ST's ideas of independent persons, the social-relationship model also downplays the need for any true or literal divine substance.