Bezier curves were invented to design physical objects (cars), but they were an idealized and simplified solution to enable CAD at the time computer were much less powerful. Ideally, CAD should put elastica curves as the first choice - but they are difficult to compute as they can diverge drastically when control points get too close, and there is sometimes more than one solution for a set of constraints.

Spiro curves were supposed to solve it but I am surprised to read here that even spiro fails to approximate elastica. Have you mapped where the limitations are?

For information, I am drawing boat hulls, and elastica would model the natural bend of wood/plywood/metal much better than bezier... Amateur naval designers really lack good tools to bridge the gap between ideal hydrodynamic forms and ease of construction, and there are still a lot of tiny but annoying adjustments when one planks the first hull.