That's exactly what I've always been curious about!

It seems vastly more intuitive to place points rather than adjust handles. (And set directions for endpoints if the curve is open.)

And obviously a practical tool will provide the capability to join separate cubic splines at sharp angles.

Does anyone know of a GUI drawing tool based on this? I've always wanted to experiment with it. Because I've always wanted to either confirm that it's a great idea that we should all be using instead of beziers, or else discover if there's an immediately obvious reason once you try it out that it's a terrible idea.