Why doesn't it have much theological promise? Good question; let me attempt a very short sketch of why I say that.
At its heart, the idea is really an attempt at rationalizing the orthodox teaching. Maybe not so much rationalizing as attempting to make the ineffable more like something we relate to more easily. Three Persons with One Nature is hard and mysterious, One Being whom we experience differently maps pretty well to our everyday experience.
That doesn't make it wrong, but it does make us wonder how a great simplification might have much promise for theological reflection. For that matter, we know that monotheists like the Jews seem perfectly able to contemplate a single Person without the elaborate (and, according to this approach, ultimately false) metaphor for our own sujective experiences of the divine. It seems, in this way, more like a big step backward than forward.
Moreover, it opens the Christian message up to Nietzsche's criticism, I think. By removing the actual, ontological divinity of Jesus (or else his actual, ontological humanity) we are left with no clear way to deal with the difficult (more like impossible) teachings. All this turning other cheeks and happy, suffering people and picking up your cross becomes crazy talk: perfect examples of the slave morality that pissed Fredrich off so much.
And the reason why Nietzsche's criticism is so on-target is, I think, simply because he is exactly right. Right, except for the claim of the actual humanity and divinity of Christ. Without that, (which is to say: if we make the entire thing the subjective analysis of our own experience), we wind up with a theology that does not engage the world as it is. And the world as it is is simply this: crosses are to be avoided at all cost, suffering sucks, only loosers turn the other cheek. We cant get past these facts on our own or, for that matter, on a subjective experience of God.
And that is basically why I think there isn't much theological promise down that path.