Is it possible to convert higher order Bézier curves to piecewise cubic Bézier curves in Inkscape?
You should look over this question on StackOverflow.com: https://stackoverflow.com/questions/30419726/simplify-high-order-bezier-curve
Now... as far as supporting higher-order curves in inkscape, Wrzlprmft is right. SVG path data only has commands for orders of the 2nd and 3rd order.
You could, in theory, build a path effect with python that pretends that a set of points are all control points of a single curve, then go through the trouble of sub-dividing that curve into cubic and quadratic curves.
I would encourage you to crack open Inkscape to view the path effect python files that already exist to use as guidance. And be prepared to be frustrated. It's a long road.