I don’t think that the trinity is an “accurate description” of what the Bible teaches. I think the hermeneutical prominence that we give to it has badly obscured and corrupted the dominant kingdom narrative. This is a matter of intense and continuing debate amongst New Testament scholars, so we should probably assume that the picture will continue to change.
The New Testament certainly takes some tentative steps in the direction of trinitarian thought by identifying Jesus with the creative Word or Wisdom of God. I think, then, that it was inevitable and right that the Greek fathers reimagined the whole Jewish narrative under very different intellectual conditions. Somehow Jesus as Lord at the right hand of God and creative Logos had to be integrated into a monotheism defined rationally rather than narratively. They came up with the trinity. That’s all well and good, but I think that a historical method needs to keep a sense of the process, and not repaint the whole of the New Testament in bright Chalcedonian colours.