God as a relationship
I may be making too much of this, but I would think that God would have to be a trinity. If He weren't, He would have to point to something outside of Himself, or something in addition to Himself, for the model of a true relationship. He would almost have to have had created Adam to solve the dilemma that would bring. God's isolation surely could not reconcile the relational aspects of our lives and the declaration that we are made in His image and, therefore, unique in the universe. We could not have been created in His image and relate to other people.
And then what of the fall-sullied relationship that we have with Him now? Would we (and He perhaps?) be forever doomed to measuring the quality of our relationships with other people through the lens of a mere two and a quarter chapters of Genesis plus the longings of a God that loved and then lost love? It would smack of some level of impotence I would think. We know that He moved and continues to be moved by the love that He is for His creatures, but the foundation of that love is not crumbling and weak. It is as firm as it ever was the members of the Trinity relate to one another in the purest and most spectacular way imaginable.
And then what of His simplicity? God is more than a loving God. God is Love. God is more than alive. God is life. God is more than a God who relates to His creation. God, Himself, is relationship. We would complicate God a great deal in every aspect of His being if He were somewhat beholden to us for the expression of His relational nature.
I just can't see any way around this. There is but God one God. That one God would be quite a bit less than who He is if it were not for the Persons that He exists as.