There are applications in CAD where I imagine working with degree 2 surfaces/curves only is going to be very tricky.
What about differentials? How do you get a change of normal, how do you get a curvature tensor? Without a continuous 2nd derivative?
Edit: In e.g. product design like e.g. cars, people want curvature continuity, i.e. C2 at minimum for their surfaces, because on machined surfaces, you see any curvature discontinuities as edges in reflected light... that's why degree 3 is kind of an industry standard.
