There are two bad properties in terms of interactivity (and for other uses). In some configurations hyperbezier explodes towards infinity or at least way outside the bounds of control points. Cubic beziers don't do that, if control points are bounded the curve will be as well. This is direct result of how cubic bezier can be calculated with series of linear interpolations. Other issue was that there were discontinuities while moving through parameter space or at least very sudden jumps, small changes of control points caused curve flip to completely different shape.