I'll agree that "a near impossibility" feels like a real big overstatement; curves are very doable and common in hand-cut glass. That's true even in my first piece, under discussion, which is chock full of curves. I talk a bit in the process diary about getting comfortable with doing curved breaks after being over-cautious with my first few bits of glass.

That said, I can see how a CNC approach could help with the speed of the process; shallow/simple curves are easy enough to do reliably, but deeper, more complex, and significantly concave curves require additional effort and planning, potentially a lot of manual work with grozing pilers to break out a concavity, and additional grinding to finish out the shape.

So being able to turn a machine process to some of those cuts would save a lot of manual effort and potentially get you right up to the final polish-grind stage in one go, which certainly sounds attractive for some kinds of design.

What you're missing is glass grinders (router) and band saws. Grinders use diamond abrasive bits and flood cooling. Glass bandsaws same deal. With those you can shape flat pieces any shape you want.

I had never heard of glass bandsaws before, but this looks amazing: https://www.youtube.com/watch?v=nyqfO7GdyJ0

But you can also cut curved glass with traditional glass scoring? And this has been so for a long time.

I tried that a couple of times, can be done. Takes skill I don't really have.