In a discussion of the "Holy Trinity: Structure of Supreme Love" in the final chapter of The Experience of God: Orthodox Dogmatic Theology, Stăniloae notes that, in spite of the ultimate mystery and incomprehensibility of the formula of three persons in one substance, nevertheless if we do not speak about God as Trinity,
we would be left with the formula for an impersonal or unipersonal god who does not possess the spirit of communion with himself, and hence is neither apt for, nor disposed towards, communion with created persons (p. 246).
The critical insight here is that apart from introducing an element of community and fellowship within the godhead, there could be no grounds for positing that God desires or is even capable of communion with created persons like you and myself. The reason for this, I take it, is something like the following.
If God is going to be God, he must be complete in himself and lacking in nothing; his being and existence cannot be impoverished or characterized by need or lack in himself. This is a universally accepted premise of ancient and medieval theology, and goes hand in hand with conceiving of God as in some sense supreme. But if God is unipersonal or impersonal, then because he naturally lacks communion or fellowship, he can neither need it or desire it. If he desired it, after all, it would presume that he had need and lacked something -- that is the very nature of desire. Therefore a unipersonal or impersonal God could never be in fellowship or communion with us, since he could never need it nor desire it in any way.
But communion and fellowship are essential components of our lives as persons. This is a repeated theme in Stăniloae's work -- that our personhood demands that our perfection address our natural impulse towards communion and fellowship. Insofar as only God can save and perfect us, God must therefore have communion and fellowship within himself:
Moreover, only through the Trinity is our eternal communion with the infinite love of God assured as such, together with the communion among ourselves as those who partake of this infinity and yet remain distinct. The Trinity thereby assures our continuance and perfection as persons to all eternity (p. 247).
For this reason the doctrine of the Trinity is an essential component of a Christian doctrine of salvation: if Christianity is to propose the salvation and perfection of human persons, then it must have a conception of God that is amenable to the essentially and paradigmatically personal need and desire for fellowship. Otherwise the spiritual life would be as Plotinus said, a flight of the alone to the Alone (Enneads VI, 9, 11).