For what it's worth, I just ended up here looking for this exact feature. +1 for true Bezier lines.

I'd also like to be able to take a Bezier shape and break it at a control point, turning it into a Bezier line. Furthermore, after intersecting two Bezier shapes, it would be helpful to maintain edit-ability of the control points.

As for implementation approaches, I'd suggest adding a fourth line type so you can ensure existing files render without visual changes between versions. You could call one "auto curvy" and the other "advanced curvy", or similar.

All that being said, the corner radius feature is very cool and can get you far.