If one doesn't make this move, a lot of doctrines of historic Christianity go by the way side. For example, where in the Bible does it say "God is one nature and three persons." That's not a specific Bible verse. But the Bible does say the Son is God, so is the Father and the Holy Ghost. Then it say, there's only one God. Combine this with the fact that each addresses the others as personal "Thous" (so Modalism is ruled out) and you've got the doctrine of the Trinity.
Also, the enhyposthesis-anhyposthesis Christology that EO, RC, Lutherans, and Reformed all accept. Where in Scripture does it say "Christ's divine nature is the person in which the human nature, (which is not person, and therefore anhyposthesis) subsists"? No where. But, Son is again and again described as the subject of the Incarnation- therefore it's a logical inference to have an enhyposthesis-anhyposthesis Christology.
Remember, during the Seminex debates, the liberals attacked the confessionalists by saying that one could not establish doctrines by inference (they were addressing a number of issues). That's one of the reasons why Robert Preus in the first volume of Post-Reformation Lutheran Dogmatics, so vigorously defends the idea when dealing with the prolegomena to dogmatics.