@mcvltd I agree a higher order single span curve/surface will have usually have smoother curvature than a lower order multi-span curve/surface with the same number of control points. So the received wisdom is to use only single span curves and surfaces for design to ensure pretty curvature.
But the tradeoff is less local control of the shape. Move any control point in a single span curve or surface of any order, and the entire curve or surface is affected, though the effect is smaller away from the control point. The single span curve/surface has the advantage that the curve/surface will tend to remain “smoother” when control points are moved. However it is more difficult, actually impossible, to limit the changes in the curve or surface to a local area.
Also, the global change behavior of single span curves and surfaces means that it is not possible to have a single span curve or surface with a portion which is straight/flat and a portion which is curved. For higher degree curves and surfaces the difference from straight/flat may be small in some areas but there will still be a difference. If the design will only be rendered or will be built with hand fitting then that difference may not matter or may be inconsequential. But if parts of an assembly, jig or mold are to be accurately machined then that difference may cause problems. This is the problem that the original poster, wynott, has encountered.
I am amused when I see claims that multiple single span curves/surfaces with matching along coincident edges to the desired level provides superior smoothness to what can be achieved with a single multi-span curve or surface of the same degree. For any polycurve made up of single span curves there is an exactly equivalent multi-span curve. For any set of single span surfaces in a “rectangular” configuration there is an exactly equivalent multi-span surface of the same degree.