These are an exciting new curve. I’d like to hear about how they will handle stroking. The inside and outside stroke of a Bézier curve can’t be represented with a Bézier curve. How do hyperbeziers fare?
This is future work, but I expect it to go fairly well. One encouraging sign is that there are parts of the parameter space where you do get an exact solution: circular arcs and circle involute. Another encouraging sign is that it's easy to get bounds on curvature, which is important for figuring out whether there's a cusp in the offset curve.