You should look over this question on StackOverflow.com: 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.
wiki.inkscape.org/wiki/index.php/Script_extensions
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.

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: How to convert higher order Bézier curves to piecewise cubic Bézier curves Is it possible to convert higher order Bézier curves to piecewise cubic Bézier curves in Inkscape?

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