Well, the answer is... there probably is not one exegetical pressure, unless we redefine exegesis in a way similar to Holmes’ suggestion at the Fuller lecture. There are exegetical pressures, plural. Some believe they lead one way, and others another culminating in one general "pressure".
But there is a third way, expounded by Ehrman and others: the authors did not all believe the same thing about Jesus. A trinitarian will say, or at least in my view should say, that is fine, God revealed different aspects to different writers, and even to the same authors different aspects at different times (e.g. nearness of Christ's second coming for Paul in 1 Thessalonians) and it is the beautiful, painstaking, complementary and collective mosaic of revelation that results in such a wonderful finale. This finale thus harmonises these perspectives into a single portrait, approximating the extraordinary fourth-century creed. The unitarians have many texts that are in favour of distinction between God and Jesus in the New Testament writers' mind that do not require in my view quite the same mosaic approach or creedal layering.
This is the assumption:
Some of this was inspired from the rather engaging debate with Buzzard and White here, where this assumption is not even laid out.